Properties

Label 95.2.i
Level $95$
Weight $2$
Character orbit 95.i
Rep. character $\chi_{95}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(95, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16 q + 6 q^{4} - 12 q^{6} + 2 q^{9} + O(q^{10}) \) \( 16 q + 6 q^{4} - 12 q^{6} + 2 q^{9} - 2 q^{10} + 6 q^{14} - 4 q^{15} - 6 q^{16} + 2 q^{19} - 32 q^{20} - 20 q^{21} + 2 q^{24} - 60 q^{26} + 6 q^{29} + 12 q^{30} + 32 q^{31} + 2 q^{34} + 16 q^{35} + 26 q^{36} + 4 q^{39} + 10 q^{40} - 16 q^{41} + 16 q^{44} + 48 q^{45} + 56 q^{46} - 40 q^{49} - 40 q^{50} - 40 q^{51} - 4 q^{54} - 20 q^{55} + 92 q^{56} + 38 q^{59} + 4 q^{60} + 16 q^{61} + 56 q^{64} - 24 q^{65} - 6 q^{66} - 36 q^{69} + 62 q^{70} - 14 q^{74} - 56 q^{75} - 74 q^{76} + 26 q^{79} - 30 q^{80} - 32 q^{81} - 96 q^{84} + 10 q^{85} + 8 q^{86} + 14 q^{89} - 32 q^{90} + 8 q^{91} - 108 q^{94} + 62 q^{95} + 52 q^{96} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.2.i.a 95.i 95.i $4$ $0.759$ \(\Q(\zeta_{12})\) None 95.2.i.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
95.2.i.b 95.i 95.i $12$ $0.759$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 95.2.i.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)