Properties

Label 2006.2.a
Level 2006
Weight 2
Character orbit a
Rep. character \(\chi_{2006}(1,\cdot)\)
Character field \(\Q\)
Dimension 79
Newforms 23
Sturm bound 540
Trace bound 5

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Defining parameters

Level: \( N \) = \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2006.a (trivial)
Character field: \(\Q\)
Newforms: \( 23 \)
Sturm bound: \(540\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2006))\).

Total New Old
Modular forms 274 79 195
Cusp forms 267 79 188
Eisenstein series 7 0 7

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

\(2\)\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(13\)
Plus space\(+\)\(28\)
Minus space\(-\)\(51\)

Trace form

\(79q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 83q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 83q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 79q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 73q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 83q^{36} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut 95q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 38q^{53} \) \(\mathstrut +\mathstrut 16q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut +\mathstrut 42q^{61} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 79q^{64} \) \(\mathstrut -\mathstrut 36q^{65} \) \(\mathstrut +\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 18q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 48q^{78} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 111q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 8q^{88} \) \(\mathstrut -\mathstrut 66q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 56q^{93} \) \(\mathstrut +\mathstrut 48q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 17q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2006))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17 59
2006.2.a.a \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-5\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-5q^{7}+\cdots\)
2006.2.a.b \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2006.2.a.c \(1\) \(16.018\) \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
2006.2.a.d \(1\) \(16.018\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
2006.2.a.e \(1\) \(16.018\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
2006.2.a.f \(1\) \(16.018\) \(\Q\) None \(-1\) \(3\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}+4q^{7}+\cdots\)
2006.2.a.g \(1\) \(16.018\) \(\Q\) None \(1\) \(-3\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}-q^{7}+\cdots\)
2006.2.a.h \(1\) \(16.018\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2006.2.a.i \(1\) \(16.018\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2006.2.a.j \(1\) \(16.018\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-6q^{11}+\cdots\)
2006.2.a.k \(1\) \(16.018\) \(\Q\) None \(1\) \(2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+2q^{7}+\cdots\)
2006.2.a.l \(2\) \(16.018\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-3q^{7}+\cdots\)
2006.2.a.m \(2\) \(16.018\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}+\beta q^{6}+\cdots\)
2006.2.a.n \(3\) \(16.018\) 3.3.229.1 None \(-3\) \(2\) \(-2\) \(3\) \(+\) \(+\) \(+\) \(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
2006.2.a.o \(3\) \(16.018\) 3.3.568.1 None \(3\) \(-1\) \(5\) \(7\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots\)
2006.2.a.p \(4\) \(16.018\) 4.4.2225.1 None \(-4\) \(-1\) \(-5\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
2006.2.a.q \(4\) \(16.018\) \(\Q(\zeta_{20})^+\) None \(-4\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
2006.2.a.r \(4\) \(16.018\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(4\) \(-4\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
2006.2.a.s \(4\) \(16.018\) 4.4.13676.1 None \(4\) \(-3\) \(3\) \(-12\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2006.2.a.t \(8\) \(16.018\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(5\) \(-5\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{7})q^{5}+\cdots\)
2006.2.a.u \(9\) \(16.018\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-1\) \(7\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots\)
2006.2.a.v \(12\) \(16.018\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-3\) \(-1\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
2006.2.a.w \(13\) \(16.018\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(7\) \(1\) \(8\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{8}q^{5}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 2}\)