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Properties

Label 462.8.g
Level $462$
Weight $8$
Character orbit 462.g
Rep. character $\chi_{462}(419,\cdot)$
Character field $\Q$
Dimension $184$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 680 184 496
Cusp forms 664 184 480
Eisenstein series 16 0 16

Trace form

\( 184 q - 11776 q^{4} - 436 q^{7} - 3016 q^{9} + O(q^{10}) \) \( 184 q - 11776 q^{4} - 436 q^{7} - 3016 q^{9} - 43264 q^{15} + 753664 q^{16} - 50624 q^{18} - 115252 q^{21} + 2625000 q^{25} + 27904 q^{28} + 229056 q^{30} + 193024 q^{36} - 1190976 q^{37} - 152848 q^{39} - 483840 q^{42} + 3292896 q^{43} - 1999936 q^{46} + 1542352 q^{49} + 4806008 q^{51} + 1762576 q^{57} - 1981440 q^{58} + 2768896 q^{60} + 5466356 q^{63} - 48234496 q^{64} - 15950160 q^{67} + 1702144 q^{70} + 3239936 q^{72} - 3386880 q^{78} - 16151352 q^{79} + 7074584 q^{81} + 7376128 q^{84} + 49229360 q^{85} - 39991400 q^{91} - 29635712 q^{93} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)