Properties

Label 385.2.c
Level $385$
Weight $2$
Character orbit 385.c
Rep. character $\chi_{385}(76,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

\( 32q - 28q^{4} - 36q^{9} + O(q^{10}) \) \( 32q - 28q^{4} - 36q^{9} + 6q^{11} + 8q^{14} - 4q^{15} + 36q^{16} - 40q^{22} + 16q^{23} - 32q^{25} + 68q^{36} + 32q^{37} - 24q^{42} + 36q^{44} - 8q^{53} - 80q^{56} - 40q^{60} - 36q^{64} - 32q^{67} - 28q^{70} + 64q^{77} + 168q^{78} - 64q^{86} + 116q^{88} + 36q^{91} - 104q^{92} - 88q^{93} - 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
385.2.c.a \(32\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)