Properties

Label 95.2.b
Level $95$
Weight $2$
Character orbit 95.b
Rep. character $\chi_{95}(39,\cdot)$
Character field $\Q$
Dimension $8$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 12 8 4
Cusp forms 8 8 0
Eisenstein series 4 0 4

Trace form

\( 8 q - 6 q^{4} - 3 q^{5} - 8 q^{9} + O(q^{10}) \) \( 8 q - 6 q^{4} - 3 q^{5} - 8 q^{9} + 8 q^{10} - 6 q^{11} - 12 q^{14} + 10 q^{15} - 6 q^{16} + 4 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{24} - 3 q^{25} + 12 q^{26} - 24 q^{29} + 24 q^{30} - 8 q^{31} + 16 q^{34} + 5 q^{35} - 26 q^{36} + 8 q^{39} - 4 q^{40} - 8 q^{41} - 28 q^{44} - 21 q^{45} + 4 q^{46} + 10 q^{49} + 4 q^{50} + 4 q^{51} + 16 q^{54} - 25 q^{55} + 52 q^{56} - 20 q^{59} + 20 q^{60} - 10 q^{61} - 2 q^{64} - 12 q^{65} - 48 q^{66} + 24 q^{69} + 16 q^{70} + 60 q^{71} + 20 q^{74} - 34 q^{75} - 10 q^{76} + 16 q^{79} - 30 q^{80} + 56 q^{81} + 24 q^{84} + 29 q^{85} - 20 q^{86} - 20 q^{89} - 40 q^{90} - 32 q^{91} + 36 q^{94} + q^{95} - 64 q^{96} + 6 q^{99} + O(q^{100}) \)

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.b.a 95.b 5.b $2$ $0.759$ \(\Q(\sqrt{-1}) \) None 95.2.b.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1+2i)q^{5}-2iq^{7}+\cdots\)
95.2.b.b 95.b 5.b $6$ $0.759$ 6.0.16516096.1 None 95.2.b.b \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)