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 $1$

Related objects

Downloads

Learn more

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

\( 8 q - 6 q^{4} - 3 q^{5} - 8 q^{9} + 8 q^{10} - 6 q^{11} - 12 q^{14} + 10 q^{15} - 6 q^{16} + 4 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{24} - 3 q^{25} + 12 q^{26} - 24 q^{29} + 24 q^{30} - 8 q^{31} + 16 q^{34}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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