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Properties

Label 110.2.g
Level $110$
Weight $2$
Character orbit 110.g
Rep. character $\chi_{110}(31,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $3$
Sturm bound $36$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 110.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(110, [\chi])\).

Total New Old
Modular forms 88 16 72
Cusp forms 56 16 40
Eisenstein series 32 0 32

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(110, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
110.2.g.a 110.g 11.c $4$ $0.878$ \(\Q(\zeta_{10})\) None \(-1\) \(4\) \(1\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
110.2.g.b 110.g 11.c $4$ $0.878$ \(\Q(\zeta_{10})\) None \(1\) \(4\) \(1\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
110.2.g.c 110.g 11.c $8$ $0.878$ 8.0.682515625.5 None \(2\) \(-4\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)