Properties

Label 930.2.bo
Level $930$
Weight $2$
Character orbit 930.bo
Rep. character $\chi_{930}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $512$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 1600 512 1088
Cusp forms 1472 512 960
Eisenstein series 128 0 128

Trace form

\( 512q - 128q^{4} + 8q^{9} + O(q^{10}) \) \( 512q - 128q^{4} + 8q^{9} - 4q^{10} + 10q^{15} - 128q^{16} - 8q^{19} - 4q^{25} + 84q^{31} + 28q^{34} + 8q^{36} + 16q^{39} + 6q^{40} - 24q^{45} - 20q^{46} - 80q^{49} + 136q^{51} - 10q^{60} - 128q^{64} + 16q^{66} + 20q^{69} - 32q^{70} - 82q^{75} - 48q^{76} + 80q^{79} + 24q^{81} - 60q^{85} - 74q^{90} - 40q^{91} + 8q^{94} + 204q^{99} + O(q^{100}) \)

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.bo.a \(256\) \(7.426\) None \(-64\) \(0\) \(-2\) \(0\)
930.2.bo.b \(256\) \(7.426\) None \(64\) \(0\) \(2\) \(0\)

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

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