Properties

Label 930.2.e
Level $930$
Weight $2$
Character orbit 930.e
Rep. character $\chi_{930}(929,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $2$
Sturm bound $384$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

Total New Old
Modular forms 200 64 136
Cusp forms 184 64 120
Eisenstein series 16 0 16

Trace form

\( 64q + 64q^{4} + 8q^{9} + O(q^{10}) \) \( 64q + 64q^{4} + 8q^{9} - 4q^{10} + 64q^{16} + 16q^{19} + 20q^{25} - 24q^{31} + 8q^{36} - 8q^{39} - 4q^{40} - 32q^{45} - 72q^{49} - 8q^{51} + 64q^{64} + 16q^{66} - 16q^{69} - 32q^{70} + 16q^{76} + 48q^{81} - 52q^{90} + 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.2.e.a \(32\) \(7.426\) None \(-32\) \(0\) \(2\) \(0\)
930.2.e.b \(32\) \(7.426\) None \(32\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)