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Properties

Label 462.8.bf
Level $462$
Weight $8$
Character orbit 462.bf
Rep. character $\chi_{462}(5,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1792$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 462.bf (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(462, [\chi])\).

Total New Old
Modular forms 5440 1792 3648
Cusp forms 5312 1792 3520
Eisenstein series 128 0 128

Trace form

\( 1792 q - 14336 q^{4} + 1348 q^{7} + 3444 q^{9} + O(q^{10}) \) \( 1792 q - 14336 q^{4} + 1348 q^{7} + 3444 q^{9} - 1248 q^{10} - 21000 q^{15} + 917504 q^{16} - 4544 q^{18} + 243584 q^{21} + 58656 q^{22} + 3687408 q^{25} + 129408 q^{28} - 57438 q^{31} + 3925524 q^{33} - 293888 q^{36} - 314612 q^{37} + 1069200 q^{39} + 119808 q^{40} - 827488 q^{42} - 4392128 q^{43} - 2389008 q^{45} - 1021888 q^{46} + 716596 q^{49} + 3092056 q^{51} - 906616 q^{57} + 2116048 q^{58} + 448000 q^{60} + 17858724 q^{63} + 117440512 q^{64} - 3713088 q^{66} + 6346336 q^{67} - 14757136 q^{70} - 436224 q^{72} + 8886432 q^{73} + 92045316 q^{75} + 38266624 q^{78} + 30751772 q^{79} - 21598840 q^{81} + 14722368 q^{82} - 10646784 q^{84} - 56689544 q^{85} - 30447876 q^{87} + 1876992 q^{88} - 18401336 q^{91} - 27848546 q^{93} + 14191488 q^{94} - 106630112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)