Properties

Label 462.2.s
Level $462$
Weight $2$
Character orbit 462.s
Rep. character $\chi_{462}(125,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $128$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
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 416 128 288
Cusp forms 352 128 224
Eisenstein series 64 0 64

Trace form

\( 128q + 32q^{4} - 4q^{7} + 12q^{9} + O(q^{10}) \) \( 128q + 32q^{4} - 4q^{7} + 12q^{9} + 12q^{15} - 32q^{16} - 16q^{18} - 20q^{21} - 36q^{25} - 6q^{28} + 8q^{36} - 16q^{37} + 60q^{39} + 4q^{42} - 64q^{43} - 8q^{46} - 40q^{49} - 28q^{51} + 88q^{57} + 92q^{58} + 8q^{60} - 42q^{63} + 32q^{64} - 64q^{67} - 26q^{70} - 24q^{72} - 64q^{78} + 136q^{79} - 116q^{81} - 28q^{85} - 40q^{91} - 76q^{93} - 160q^{99} + O(q^{100}) \)

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.s.a \(128\) \(3.689\) None \(0\) \(0\) \(0\) \(-4\)

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

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