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Properties

Label 115.2.g
Level $115$
Weight $2$
Character orbit 115.g
Rep. character $\chi_{115}(6,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $80$
Newform subspaces $3$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.g (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(115, [\chi])\).

Total New Old
Modular forms 140 80 60
Cusp forms 100 80 20
Eisenstein series 40 0 40

Trace form

\( 80 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 14 q^{6} - 4 q^{7} - 18 q^{8} - 12 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 14 q^{6} - 4 q^{7} - 18 q^{8} - 12 q^{9} - 6 q^{10} - 16 q^{11} - 6 q^{12} - 4 q^{13} - 12 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 42 q^{18} + 6 q^{19} - 6 q^{20} + 22 q^{21} + 16 q^{22} - 18 q^{23} + 96 q^{24} - 8 q^{25} - 10 q^{26} + 30 q^{27} - 48 q^{28} - 24 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 48 q^{33} - 22 q^{34} + 16 q^{35} + 8 q^{36} - 40 q^{37} + 22 q^{38} - 20 q^{39} + 58 q^{40} - 6 q^{41} - 104 q^{42} + 56 q^{43} - 30 q^{44} + 40 q^{45} + 104 q^{46} - 64 q^{47} + 86 q^{48} + 8 q^{49} + 18 q^{50} + 20 q^{51} - 66 q^{52} - 28 q^{53} + 12 q^{54} + 28 q^{55} + 80 q^{56} - 14 q^{57} + 68 q^{58} - 4 q^{59} + 10 q^{60} - 12 q^{61} + 70 q^{62} + 18 q^{63} - 62 q^{64} - 24 q^{65} - 92 q^{66} - 32 q^{67} + 112 q^{68} - 96 q^{69} - 12 q^{70} - 66 q^{71} + 18 q^{72} - 4 q^{73} - 38 q^{74} - 24 q^{76} + 90 q^{77} + 158 q^{78} + 40 q^{79} - 30 q^{80} - 60 q^{81} + 78 q^{82} + 86 q^{83} + 134 q^{84} - 18 q^{85} - 102 q^{86} + 152 q^{87} - 16 q^{88} + 28 q^{89} - 42 q^{90} - 68 q^{91} + 42 q^{92} + 148 q^{93} + 32 q^{94} - 16 q^{95} - 162 q^{96} + 56 q^{97} - 12 q^{98} + 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.2.g.a 115.g 23.c $10$ $0.918$ \(\Q(\zeta_{22})\) None 115.2.g.a \(5\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
115.2.g.b 115.g 23.c $20$ $0.918$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 115.2.g.b \(-4\) \(1\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots\)
115.2.g.c 115.g 23.c $50$ $0.918$ None 115.2.g.c \(-5\) \(-2\) \(-5\) \(-5\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(115, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)