Properties

Label 95.3.d
Level $95$
Weight $3$
Character orbit 95.d
Rep. character $\chi_{95}(94,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $4$
Sturm bound $30$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 95.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(95, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

Trace form

\( 18q + 32q^{4} - q^{5} - 8q^{6} + 38q^{9} + O(q^{10}) \) \( 18q + 32q^{4} - q^{5} - 8q^{6} + 38q^{9} - 22q^{11} + 72q^{16} + 10q^{19} + 60q^{20} - 256q^{24} + 55q^{25} - 176q^{26} - 264q^{30} + 41q^{35} + 32q^{36} + 184q^{39} - 144q^{44} + 33q^{45} + 164q^{49} - 13q^{55} - 30q^{61} + 392q^{64} + 168q^{66} + 384q^{74} - 24q^{76} + 256q^{80} + 594q^{81} + 195q^{85} - 597q^{95} - 1312q^{96} - 1178q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
95.3.d.a \(2\) \(2.589\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(0\) \(q-4q^{4}+(-4-\beta )q^{5}+(-3+6\beta )q^{7}+\cdots\)
95.3.d.b \(4\) \(2.589\) 4.4.462080.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(-20\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(4+\beta _{3})q^{4}+\cdots\)
95.3.d.c \(4\) \(2.589\) 4.4.7600.1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(20\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(4+3\beta _{3})q^{4}+\cdots\)
95.3.d.d \(8\) \(2.589\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+2\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)