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

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

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

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