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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

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
95.2.b.a \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}+q^{4}+(-1+2i)q^{5}-2iq^{7}+\cdots\)
95.2.b.b \(6\) \(0.759\) 6.0.16516096.1 None \(0\) \(0\) \(-1\) \(0\) \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)