Properties

Label 380.3.g
Level $380$
Weight $3$
Character orbit 380.g
Rep. character $\chi_{380}(189,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $3$
Sturm bound $180$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 380.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 126 20 106
Cusp forms 114 20 94
Eisenstein series 12 0 12

Trace form

\( 20q + q^{5} + 60q^{9} + O(q^{10}) \) \( 20q + q^{5} + 60q^{9} - 2q^{11} - 28q^{19} - 7q^{25} - 71q^{35} - 96q^{39} + 39q^{45} - 26q^{49} - 33q^{55} + 6q^{61} + 412q^{81} + 139q^{85} + 53q^{95} + 162q^{99} + O(q^{100}) \)

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.g.a \(4\) \(10.354\) \(\Q(\sqrt{-6}, \sqrt{14})\) None \(0\) \(0\) \(-20\) \(0\) \(q-\beta _{1}q^{3}-5q^{5}+\beta _{2}q^{7}+5q^{9}+4q^{11}+\cdots\)
380.3.g.b \(4\) \(10.354\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(9\) \(0\) \(q+(2-\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{7}-9q^{9}+\cdots\)
380.3.g.c \(12\) \(10.354\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) \(q-\beta _{5}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)

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

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