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Properties

Label 462.4.n
Level $462$
Weight $4$
Character orbit 462.n
Rep. character $\chi_{462}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 592 192 400
Cusp forms 560 192 368
Eisenstein series 32 0 32

Trace form

\( 192 q - 384 q^{4} - 64 q^{9} + O(q^{10}) \) \( 192 q - 384 q^{4} - 64 q^{9} - 160 q^{15} - 1536 q^{16} + 312 q^{22} + 2244 q^{25} + 48 q^{27} - 276 q^{31} - 4 q^{33} + 240 q^{34} + 512 q^{36} - 300 q^{37} + 144 q^{42} + 304 q^{45} + 684 q^{49} - 204 q^{55} + 1008 q^{58} + 320 q^{60} + 12288 q^{64} + 368 q^{66} - 504 q^{67} + 560 q^{69} + 840 q^{70} + 488 q^{75} + 1632 q^{78} + 1008 q^{81} + 768 q^{82} - 624 q^{88} - 2520 q^{91} + 304 q^{93} - 4320 q^{97} + 3444 q^{99} + O(q^{100}) \)

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

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