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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
190.3.d.a 190.d 95.d $20$ $5.177$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+2q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)

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

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