Properties

Label 5610.2.a
Level $5610$
Weight $2$
Character orbit 5610.a
Rep. character $\chi_{5610}(1,\cdot)$
Character field $\Q$
Dimension $111$
Newform subspaces $63$
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: \(\Q\)
Newform subspaces: \( 63 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\) into newform subspaces

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

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

\( S_{2}^{\mathrm{old}}(\Gamma_0(5610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2805))\)\(^{\oplus 2}\)