Properties

Label 380.2.r
Level $380$
Weight $2$
Character orbit 380.r
Rep. character $\chi_{380}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 132 20 112
Cusp forms 108 20 88
Eisenstein series 24 0 24

Trace form

\( 20 q + q^{5} + 10 q^{9} + O(q^{10}) \) \( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65} + 48 q^{69} - 2 q^{71} + 46 q^{75} - 16 q^{79} + 26 q^{81} - 39 q^{85} - 40 q^{89} - 4 q^{91} - 43 q^{95} - 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.r.a $20$ $3.034$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(1\) \(0\) \(q+(\beta _{1}-\beta _{11})q^{3}+(-\beta _{7}+\beta _{13})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

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