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Properties

Label 462.4.s
Level $462$
Weight $4$
Character orbit 462.s
Rep. character $\chi_{462}(125,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $384$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 462.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(462, [\chi])\).

Total New Old
Modular forms 1184 384 800
Cusp forms 1120 384 736
Eisenstein series 64 0 64

Trace form

\( 384 q + 384 q^{4} + 12 q^{7} - 96 q^{9} + O(q^{10}) \) \( 384 q + 384 q^{4} + 12 q^{7} - 96 q^{9} + 120 q^{15} - 1536 q^{16} + 224 q^{18} + 280 q^{21} + 240 q^{22} - 2460 q^{25} + 72 q^{28} - 256 q^{36} - 48 q^{37} - 180 q^{39} - 1304 q^{42} + 2688 q^{43} - 432 q^{46} + 120 q^{49} - 892 q^{51} - 1904 q^{57} - 3192 q^{58} + 320 q^{60} + 1428 q^{63} + 6144 q^{64} + 4032 q^{67} - 1380 q^{70} + 1344 q^{72} + 2816 q^{78} - 1224 q^{79} + 4192 q^{81} - 720 q^{84} - 10548 q^{85} - 960 q^{88} + 24 q^{91} - 4456 q^{93} + 11648 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

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