Properties

Label 462.2.bf
Level $462$
Weight $2$
Character orbit 462.bf
Rep. character $\chi_{462}(5,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.bf (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(462, [\chi])\).

Total New Old
Modular forms 832 256 576
Cusp forms 704 256 448
Eisenstein series 128 0 128

Trace form

\( 256q - 32q^{4} + 4q^{7} - 12q^{9} + O(q^{10}) \) \( 256q - 32q^{4} + 4q^{7} - 12q^{9} + 12q^{10} + 24q^{15} + 32q^{16} - 8q^{18} - 16q^{21} - 12q^{22} + 48q^{25} + 6q^{28} + 18q^{31} - 132q^{33} + 16q^{36} + 4q^{37} - 18q^{40} - 4q^{42} + 64q^{43} - 48q^{45} + 8q^{46} + 76q^{49} - 8q^{51} - 88q^{57} + 46q^{58} - 8q^{60} - 12q^{63} + 64q^{64} - 120q^{66} - 32q^{67} - 58q^{70} - 12q^{72} - 96q^{73} - 204q^{75} - 32q^{78} - 4q^{79} - 64q^{81} + 24q^{82} - 36q^{84} + 232q^{85} - 228q^{87} - 6q^{88} + 40q^{91} - 2q^{93} - 144q^{94} + 160q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
462.2.bf.a \(256\) \(3.689\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)