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Properties

Label 462.4.bf
Level $462$
Weight $4$
Character orbit 462.bf
Rep. character $\chi_{462}(5,\cdot)$
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.bf (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

\( 768 q - 384 q^{4} - 12 q^{7} + 96 q^{9} + O(q^{10}) \) \( 768 q - 384 q^{4} - 12 q^{7} + 96 q^{9} + 72 q^{10} + 240 q^{15} + 1536 q^{16} + 112 q^{18} + 440 q^{21} - 24 q^{22} + 2208 q^{25} - 72 q^{28} + 1242 q^{31} + 3468 q^{33} - 512 q^{36} + 300 q^{37} - 660 q^{39} - 432 q^{40} + 1304 q^{42} - 2688 q^{43} + 1392 q^{45} + 432 q^{46} - 2604 q^{49} - 1628 q^{51} + 1904 q^{57} - 1596 q^{58} - 320 q^{60} - 7152 q^{63} + 12288 q^{64} - 2064 q^{66} + 2016 q^{67} + 1884 q^{70} + 672 q^{72} - 4608 q^{73} + 5016 q^{75} + 4288 q^{78} + 5004 q^{79} - 2428 q^{81} - 432 q^{82} + 1440 q^{84} + 3096 q^{85} - 4980 q^{87} - 48 q^{88} - 8088 q^{91} - 6296 q^{93} + 11232 q^{94} - 11396 q^{99} + O(q^{100}) \)

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

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