Properties

Label 380.2.c
Level $380$
Weight $2$
Character orbit 380.c
Rep. character $\chi_{380}(229,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 66 10 56
Cusp forms 54 10 44
Eisenstein series 12 0 12

Trace form

\( 10q - q^{5} - 10q^{9} + O(q^{10}) \) \( 10q - q^{5} - 10q^{9} + 6q^{11} - 10q^{15} - 2q^{19} - 4q^{21} + 15q^{25} + 4q^{29} - 8q^{31} - 13q^{35} + 32q^{39} - 20q^{41} - 7q^{45} - 16q^{49} + 28q^{51} + 21q^{55} - 4q^{59} + 10q^{61} - 12q^{65} + 20q^{71} - 46q^{75} - 32q^{79} + 34q^{81} - 15q^{85} + 16q^{89} + 16q^{91} + q^{95} - 70q^{99} + O(q^{100}) \)

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.c.a \(4\) \(3.034\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
380.2.c.b \(6\) \(3.034\) 6.0.14077504.2 None \(0\) \(0\) \(-1\) \(0\) \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)

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

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