Properties

Label 462.8.s
Level $462$
Weight $8$
Character orbit 462.s
Rep. character $\chi_{462}(125,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $896$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 2720 896 1824
Cusp forms 2656 896 1760
Eisenstein series 64 0 64

Trace form

\( 896 q + 14336 q^{4} - 1348 q^{7} - 3444 q^{9} + O(q^{10}) \) \( 896 q + 14336 q^{4} - 1348 q^{7} - 3444 q^{9} - 10500 q^{15} - 917504 q^{16} - 9088 q^{18} - 1700 q^{21} - 49920 q^{22} - 3718140 q^{25} - 129408 q^{28} - 146944 q^{36} - 135472 q^{37} + 2685660 q^{39} + 827488 q^{42} + 4392128 q^{43} + 1021888 q^{46} - 6439480 q^{49} + 4331828 q^{51} + 906616 q^{57} + 4232096 q^{58} - 448000 q^{60} + 3492174 q^{63} + 58720256 q^{64} + 12692672 q^{67} - 16082960 q^{70} - 872448 q^{72} - 6134272 q^{78} - 4158584 q^{79} - 1521332 q^{81} - 13063680 q^{84} + 57996332 q^{85} + 3194880 q^{88} + 9797048 q^{91} + 37568612 q^{93} + 113573216 q^{99} + O(q^{100}) \)

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

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