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Properties

Label 462.4.bc
Level $462$
Weight $4$
Character orbit 462.bc
Rep. character $\chi_{462}(95,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.bc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 2368 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

Trace form

\( 768 q + 384 q^{4} - 96 q^{9} + O(q^{10}) \) \( 768 q + 384 q^{4} - 96 q^{9} - 240 q^{15} + 1536 q^{16} - 312 q^{22} - 2424 q^{25} + 72 q^{27} + 120 q^{28} - 414 q^{31} - 1596 q^{33} + 960 q^{34} - 512 q^{36} + 300 q^{37} - 460 q^{39} + 240 q^{40} - 1304 q^{42} - 304 q^{45} - 2604 q^{49} + 260 q^{51} + 204 q^{55} - 560 q^{57} + 1932 q^{58} - 320 q^{60} - 960 q^{61} - 4000 q^{63} - 12288 q^{64} - 1728 q^{66} - 2016 q^{67} + 3440 q^{69} + 1020 q^{70} + 1120 q^{72} + 2460 q^{73} + 5432 q^{75} + 4288 q^{78} + 2812 q^{81} - 768 q^{82} + 800 q^{84} - 10200 q^{85} + 624 q^{88} - 16960 q^{90} + 2520 q^{91} - 6184 q^{93} - 6240 q^{94} + 4320 q^{97} + 12236 q^{99} + O(q^{100}) \)

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

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