Properties

Label 380.3.e
Level $380$
Weight $3$
Character orbit 380.e
Rep. character $\chi_{380}(341,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 380.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(380, [\chi])\).

Total New Old
Modular forms 126 12 114
Cusp forms 114 12 102
Eisenstein series 12 0 12

Trace form

\( 12 q - 12 q^{7} - 16 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{7} - 16 q^{9} - 32 q^{11} - 12 q^{17} + 24 q^{19} + 4 q^{23} + 60 q^{25} + 40 q^{35} + 124 q^{39} - 176 q^{43} - 40 q^{45} - 72 q^{47} - 24 q^{49} + 140 q^{57} + 152 q^{61} + 48 q^{63} - 148 q^{73} + 376 q^{77} - 468 q^{81} - 208 q^{83} - 84 q^{87} - 184 q^{93} + 392 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.3.e.a $12$ $10.354$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(-1+\beta _{6}-\beta _{11})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)