Properties

Label 5610.2.a
Level 5610
Weight 2
Character orbit a
Rep. character \(\chi_{5610}(1,\cdot)\)
Character field \(\Q\)
Dimension 111
Newforms 63
Sturm bound 2592
Trace bound 13

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Defining parameters

Level: \( N \) = \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5610.a (trivial)
Character field: \(\Q\)
Newforms: \( 63 \)
Sturm bound: \(2592\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5610))\).

Total New Old
Modular forms 1312 111 1201
Cusp forms 1281 111 1170
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.

\(2\)\(3\)\(5\)\(11\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(44\)
Minus space\(-\)\(67\)

Trace form

\( 111q - q^{2} + 7q^{3} + 111q^{4} - q^{5} - q^{6} + 8q^{7} - q^{8} + 111q^{9} + O(q^{10}) \) \( 111q - q^{2} + 7q^{3} + 111q^{4} - q^{5} - q^{6} + 8q^{7} - q^{8} + 111q^{9} - q^{10} - q^{11} + 7q^{12} + 2q^{13} - 8q^{14} - q^{15} + 111q^{16} - q^{17} - q^{18} - 4q^{19} - q^{20} + 8q^{21} + 7q^{22} - 8q^{23} - q^{24} + 111q^{25} + 2q^{26} + 7q^{27} + 8q^{28} - 30q^{29} - q^{30} - q^{32} - q^{33} - q^{34} - 8q^{35} + 111q^{36} + 26q^{37} + 28q^{38} + 34q^{39} - q^{40} + 22q^{41} - 8q^{42} + 36q^{43} - q^{44} - q^{45} + 8q^{46} + 16q^{47} + 7q^{48} + 119q^{49} - q^{50} - q^{51} + 2q^{52} + 26q^{53} - q^{54} - q^{55} - 8q^{56} + 28q^{57} + 2q^{58} + 20q^{59} - q^{60} + 18q^{61} + 32q^{62} + 8q^{63} + 111q^{64} + 18q^{65} - q^{66} + 60q^{67} - q^{68} + 8q^{69} - 8q^{70} + 8q^{71} - q^{72} + 6q^{73} - 6q^{74} + 7q^{75} - 4q^{76} + 8q^{77} + 2q^{78} + 64q^{79} - q^{80} + 111q^{81} + 22q^{82} + 44q^{83} + 8q^{84} - q^{85} + 68q^{86} + 34q^{87} + 7q^{88} - 26q^{89} - q^{90} - 16q^{91} - 8q^{92} + 16q^{93} + 16q^{94} - 20q^{95} - q^{96} + 30q^{97} + 71q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\) 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 5 11 17
5610.2.a.a \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.b \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.c \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.d \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
5610.2.a.e \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.f \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
5610.2.a.g \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.h \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5610.2.a.i \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
5610.2.a.j \(1\) \(44.796\) \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
5610.2.a.k \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.l \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
5610.2.a.m \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.n \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5610.2.a.o \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.p \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.q \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.r \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.s \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.t \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.u \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5610.2.a.v \(1\) \(44.796\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.w \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5610.2.a.x \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.y \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.z \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
5610.2.a.ba \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
5610.2.a.bb \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5610.2.a.bc \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bd \(1\) \(44.796\) \(\Q\) None \(1\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
5610.2.a.be \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bf \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bg \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
5610.2.a.bh \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bi \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
5610.2.a.bj \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(-1\) \(5\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+5q^{7}+\cdots\)
5610.2.a.bk \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
5610.2.a.bl \(1\) \(44.796\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5610.2.a.bm \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bn \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bo \(2\) \(44.796\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.bp \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(-2\) \(1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.bq \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta q^{7}+\cdots\)
5610.2.a.br \(2\) \(44.796\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bs \(2\) \(44.796\) \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bt \(2\) \(44.796\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5610.2.a.bu \(2\) \(44.796\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5610.2.a.bv \(2\) \(44.796\) \(\Q(\sqrt{41}) \) None \(2\) \(-2\) \(2\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.bw \(2\) \(44.796\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5610.2.a.bx \(2\) \(44.796\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)
5610.2.a.by \(3\) \(44.796\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.bz \(3\) \(44.796\) 3.3.148.1 None \(-3\) \(3\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.ca \(3\) \(44.796\) 3.3.961.1 None \(-3\) \(3\) \(3\) \(1\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.cb \(3\) \(44.796\) 3.3.2089.1 None \(-3\) \(3\) \(3\) \(3\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.cc \(3\) \(44.796\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5610.2.a.cd \(3\) \(44.796\) 3.3.2089.1 None \(3\) \(3\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ce \(4\) \(44.796\) 4.4.2777.1 None \(-4\) \(-4\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)
5610.2.a.cf \(4\) \(44.796\) 4.4.17428.1 None \(-4\) \(4\) \(-4\) \(5\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
5610.2.a.cg \(4\) \(44.796\) 4.4.54764.1 None \(4\) \(-4\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5610.2.a.ch \(4\) \(44.796\) 4.4.65905.1 None \(4\) \(4\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{2}q^{7}+\cdots\)
5610.2.a.ci \(5\) \(44.796\) 5.5.18569692.1 None \(5\) \(-5\) \(5\) \(2\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-\beta _{3}q^{7}+\cdots\)
5610.2.a.cj \(5\) \(44.796\) 5.5.1284160.1 None \(5\) \(5\) \(5\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
5610.2.a.ck \(5\) \(44.796\) 5.5.19985813.1 None \(5\) \(5\) \(5\) \(2\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\)\(^{\oplus 2}\)