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

\( 80 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 14 q^{6} - 4 q^{7} - 18 q^{8} - 12 q^{9} - 6 q^{10} - 16 q^{11} - 6 q^{12} - 4 q^{13} - 12 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 42 q^{18} + 6 q^{19} - 6 q^{20}+ \cdots + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

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