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Properties

Label 462.4.w
Level $462$
Weight $4$
Character orbit 462.w
Rep. character $\chi_{462}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
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.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 288 896
Cusp forms 1120 288 832
Eisenstein series 64 0 64

Trace form

\( 288 q + 4 q^{3} - 288 q^{4} + 100 q^{6} - 52 q^{9} + O(q^{10}) \) \( 288 q + 4 q^{3} - 288 q^{4} + 100 q^{6} - 52 q^{9} - 144 q^{12} + 252 q^{15} - 1152 q^{16} + 460 q^{18} - 900 q^{19} + 144 q^{22} - 400 q^{24} + 540 q^{25} - 1064 q^{27} + 1560 q^{30} + 1296 q^{31} + 370 q^{33} - 1008 q^{34} + 632 q^{36} + 216 q^{37} - 1060 q^{39} - 2184 q^{45} + 720 q^{46} + 64 q^{48} + 3528 q^{49} - 1190 q^{51} - 1920 q^{52} - 3672 q^{55} + 1390 q^{57} - 864 q^{58} + 208 q^{60} + 1800 q^{61} - 4608 q^{64} - 640 q^{66} + 13512 q^{67} + 6428 q^{69} - 1008 q^{70} + 360 q^{73} - 6470 q^{75} - 2720 q^{78} - 4680 q^{79} - 1612 q^{81} - 5976 q^{82} - 2240 q^{84} - 1620 q^{85} + 576 q^{88} + 2600 q^{90} + 3024 q^{91} + 8720 q^{93} + 16236 q^{97} + 2576 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)