Properties

Label 462.2.bc
Level $462$
Weight $2$
Character orbit 462.bc
Rep. character $\chi_{462}(95,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.bc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

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

\( 256q + 32q^{4} + 12q^{9} + O(q^{10}) \) \( 256q + 32q^{4} + 12q^{9} - 24q^{15} + 32q^{16} + 4q^{22} - 24q^{25} - 36q^{27} - 10q^{28} - 6q^{31} + 24q^{33} - 32q^{34} + 16q^{36} + 4q^{37} + 20q^{39} + 10q^{40} + 4q^{42} + 56q^{45} + 76q^{49} + 20q^{51} - 84q^{55} - 80q^{57} - 38q^{58} - 8q^{60} + 80q^{61} - 100q^{63} - 64q^{64} - 48q^{66} + 32q^{67} - 136q^{69} - 42q^{70} - 20q^{72} + 20q^{73} - 28q^{75} - 32q^{78} - 56q^{81} - 16q^{82} - 40q^{84} - 200q^{85} - 2q^{88} - 160q^{90} + 24q^{91} + 14q^{93} + 80q^{94} - 32q^{97} - 136q^{99} + O(q^{100}) \)

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.bc.a \(128\) \(3.689\) None \(-16\) \(0\) \(0\) \(0\)
462.2.bc.b \(128\) \(3.689\) None \(16\) \(0\) \(0\) \(0\)

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

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