Properties

Label 930.2.bj
Level $930$
Weight $2$
Character orbit 930.bj
Rep. character $\chi_{930}(277,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $256$
Newform subspaces $2$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

Trace form

\( 256q - 12q^{7} + O(q^{10}) \) \( 256q - 12q^{7} - 8q^{10} + 64q^{16} + 80q^{21} + 20q^{22} - 16q^{25} - 8q^{28} + 40q^{31} + 8q^{33} + 48q^{35} - 256q^{36} - 32q^{38} - 48q^{41} + 20q^{42} + 40q^{46} + 96q^{47} - 48q^{50} + 80q^{53} + 80q^{55} - 8q^{62} - 8q^{63} + 120q^{65} - 24q^{66} - 64q^{67} + 56q^{70} + 48q^{71} + 80q^{73} - 48q^{76} + 40q^{77} + 64q^{81} - 32q^{82} - 200q^{85} - 40q^{87} - 80q^{91} - 16q^{93} + 16q^{95} + 128q^{97} - 32q^{98} + O(q^{100}) \)

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.bj.a \(128\) \(7.426\) None \(0\) \(0\) \(0\) \(-16\)
930.2.bj.b \(128\) \(7.426\) None \(0\) \(0\) \(0\) \(4\)

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)