Properties

Label 6006.2.a
Level 6006
Weight 2
Character orbit a
Rep. character \(\chi_{6006}(1,\cdot)\)
Character field \(\Q\)
Dimension 119
Newforms 59
Sturm bound 2688
Trace bound 17

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Defining parameters

Level: \( N \) = \( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6006.a (trivial)
Character field: \(\Q\)
Newforms: \( 59 \)
Sturm bound: \(2688\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(17\), \(19\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6006))\).

Total New Old
Modular forms 1360 119 1241
Cusp forms 1329 119 1210
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(44\)
Minus space\(-\)\(75\)

Trace form

\(119q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 119q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(119q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 119q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 119q^{16} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut -\mathstrut q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut -\mathstrut q^{24} \) \(\mathstrut +\mathstrut 105q^{25} \) \(\mathstrut -\mathstrut q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 119q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 119q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut q^{56} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 119q^{64} \) \(\mathstrut +\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut +\mathstrut 86q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 33q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 119q^{81} \) \(\mathstrut -\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 108q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut +\mathstrut 52q^{85} \) \(\mathstrut +\mathstrut 20q^{86} \) \(\mathstrut +\mathstrut 18q^{87} \) \(\mathstrut -\mathstrut q^{88} \) \(\mathstrut +\mathstrut 38q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 136q^{95} \) \(\mathstrut -\mathstrut q^{96} \) \(\mathstrut +\mathstrut 94q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6006))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 11 13
6006.2.a.a \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.b \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.c \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.d \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.e \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
6006.2.a.f \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
6006.2.a.g \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.h \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.i \(1\) \(47.958\) \(\Q\) None \(-1\) \(-1\) \(4\) \(1\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.j \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.k \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.l \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.m \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
6006.2.a.n \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
6006.2.a.o \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
6006.2.a.p \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
6006.2.a.q \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
6006.2.a.r \(1\) \(47.958\) \(\Q\) None \(-1\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.s \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.t \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.u \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
6006.2.a.v \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
6006.2.a.w \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
6006.2.a.x \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
6006.2.a.y \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
6006.2.a.z \(1\) \(47.958\) \(\Q\) None \(1\) \(-1\) \(4\) \(1\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.ba \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.bb \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.bc \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.bd \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.be \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.bf \(1\) \(47.958\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.bg \(2\) \(47.958\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-4\) \(2\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.bh \(2\) \(47.958\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
6006.2.a.bi \(2\) \(47.958\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
6006.2.a.bj \(2\) \(47.958\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
6006.2.a.bk \(2\) \(47.958\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.bl \(2\) \(47.958\) \(\Q(\sqrt{13}) \) None \(2\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
6006.2.a.bm \(2\) \(47.958\) \(\Q(\sqrt{6}) \) None \(2\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.bn \(2\) \(47.958\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
6006.2.a.bo \(2\) \(47.958\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.bp \(2\) \(47.958\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(4\) \(2\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
6006.2.a.bq \(3\) \(47.958\) 3.3.568.1 None \(-3\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.br \(3\) \(47.958\) 3.3.621.1 None \(-3\) \(-3\) \(0\) \(3\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
6006.2.a.bs \(3\) \(47.958\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(2\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots\)
6006.2.a.bt \(3\) \(47.958\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
6006.2.a.bu \(3\) \(47.958\) 3.3.316.1 None \(3\) \(3\) \(-2\) \(3\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
6006.2.a.bv \(3\) \(47.958\) 3.3.316.1 None \(3\) \(3\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
6006.2.a.bw \(4\) \(47.958\) 4.4.2225.1 None \(-4\) \(-4\) \(-4\) \(4\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
6006.2.a.bx \(4\) \(47.958\) 4.4.15188.1 None \(-4\) \(-4\) \(2\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.by \(4\) \(47.958\) 4.4.13068.1 None \(-4\) \(-4\) \(4\) \(4\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}+q^{6}+\cdots\)
6006.2.a.bz \(4\) \(47.958\) 4.4.34196.1 None \(-4\) \(4\) \(0\) \(4\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.ca \(4\) \(47.958\) 4.4.9248.1 None \(-4\) \(4\) \(0\) \(4\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.cb \(4\) \(47.958\) 4.4.19664.1 None \(-4\) \(4\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{3})q^{5}-q^{6}+\cdots\)
6006.2.a.cc \(4\) \(47.958\) 4.4.21200.1 None \(-4\) \(4\) \(6\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
6006.2.a.cd \(4\) \(47.958\) 4.4.46912.1 None \(4\) \(4\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.ce \(4\) \(47.958\) 4.4.20308.1 None \(4\) \(4\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{7}+\cdots\)
6006.2.a.cf \(6\) \(47.958\) 6.6.72306708.1 None \(6\) \(-6\) \(0\) \(6\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+q^{7}+\cdots\)
6006.2.a.cg \(7\) \(47.958\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(2\) \(7\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1001))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2002))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3003))\)\(^{\oplus 2}\)