Properties

Label 760.2.k
Level $760$
Weight $2$
Character orbit 760.k
Rep. character $\chi_{760}(229,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

Total New Old
Modular forms 124 108 16
Cusp forms 116 108 8
Eisenstein series 8 0 8

Trace form

\( 108q + 108q^{9} + O(q^{10}) \) \( 108q + 108q^{9} - 8q^{10} - 8q^{14} + 8q^{16} - 8q^{24} + 4q^{25} + 44q^{30} + 40q^{34} - 48q^{36} - 32q^{39} - 4q^{40} - 8q^{41} + 24q^{44} + 16q^{46} - 108q^{49} - 64q^{50} - 72q^{54} - 32q^{55} + 24q^{56} - 4q^{60} - 24q^{64} - 24q^{65} - 64q^{66} + 36q^{70} + 32q^{71} + 48q^{74} + 28q^{80} + 92q^{81} + 16q^{84} - 56q^{86} - 56q^{89} - 28q^{90} - 64q^{94} + 16q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
760.2.k.a \(108\) \(6.069\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)