Properties

Label 462.2.w
Level $462$
Weight $2$
Character orbit 462.w
Rep. character $\chi_{462}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
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.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 416 96 320
Cusp forms 352 96 256
Eisenstein series 64 0 64

Trace form

\( 96q - 8q^{3} - 24q^{4} + 10q^{6} + 20q^{9} + O(q^{10}) \) \( 96q - 8q^{3} - 24q^{4} + 10q^{6} + 20q^{9} + 12q^{12} + 12q^{15} - 24q^{16} + 10q^{18} + 60q^{19} - 16q^{22} - 10q^{24} + 36q^{25} + 16q^{27} - 60q^{30} - 64q^{31} + 10q^{33} - 8q^{34} - 10q^{36} - 40q^{37} - 40q^{39} + 24q^{45} + 40q^{46} - 8q^{48} + 24q^{49} + 10q^{51} + 40q^{52} + 32q^{55} + 10q^{57} + 16q^{58} - 8q^{60} - 40q^{61} - 24q^{64} + 32q^{66} + 72q^{67} - 40q^{69} - 8q^{70} - 40q^{73} + 10q^{75} - 32q^{78} - 40q^{79} - 28q^{81} - 20q^{82} - 20q^{84} + 20q^{85} - 16q^{88} - 100q^{90} - 72q^{91} + 8q^{93} - 4q^{97} + 44q^{99} + O(q^{100}) \)

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.w.a \(48\) \(3.689\) None \(-12\) \(-4\) \(0\) \(0\)
462.2.w.b \(48\) \(3.689\) None \(12\) \(-4\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)