Properties

Label 190.3.d
Level $190$
Weight $3$
Character orbit 190.d
Rep. character $\chi_{190}(189,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 190.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(190, [\chi])\).

Total New Old
Modular forms 64 20 44
Cusp forms 56 20 36
Eisenstein series 8 0 8

Trace form

\( 20q + 40q^{4} - 2q^{5} + 60q^{9} + O(q^{10}) \) \( 20q + 40q^{4} - 2q^{5} + 60q^{9} + 28q^{11} + 80q^{16} + 20q^{19} - 4q^{20} - 82q^{25} + 32q^{26} + 88q^{30} + 142q^{35} + 120q^{36} - 288q^{39} + 56q^{44} - 174q^{45} - 440q^{49} - 144q^{54} - 54q^{55} - 12q^{61} + 160q^{64} - 544q^{66} + 40q^{76} - 8q^{80} - 380q^{81} - 266q^{85} + 434q^{95} + 1044q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(190, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
190.3.d.a \(20\) \(5.177\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(190, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)