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Properties

Label 464.4.bc
Level $464$
Weight $4$
Character orbit 464.bc
Rep. character $\chi_{464}(11,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2136$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 464.bc (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 464 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(464, [\chi])\).

Total New Old
Modular forms 2184 2184 0
Cusp forms 2136 2136 0
Eisenstein series 48 48 0

Trace form

\( 2136 q - 14 q^{2} - 10 q^{3} - 14 q^{4} - 14 q^{5} + 18 q^{6} - 20 q^{7} - 14 q^{8} - 3132 q^{9} + O(q^{10}) \) \( 2136 q - 14 q^{2} - 10 q^{3} - 14 q^{4} - 14 q^{5} + 18 q^{6} - 20 q^{7} - 14 q^{8} - 3132 q^{9} + 4 q^{10} + 126 q^{11} + 120 q^{12} - 14 q^{13} - 66 q^{14} + 108 q^{15} - 310 q^{16} - 24 q^{17} - 1646 q^{18} - 10 q^{19} - 10 q^{20} + 98 q^{21} - 46 q^{22} - 20 q^{23} - 10 q^{24} + 552 q^{26} + 362 q^{27} - 420 q^{28} + 188 q^{29} - 556 q^{30} - 254 q^{32} - 28 q^{33} + 166 q^{34} - 14 q^{35} - 396 q^{36} - 14 q^{37} + 18 q^{38} + 576 q^{39} - 552 q^{40} - 4852 q^{42} - 14 q^{43} + 254 q^{44} + 490 q^{45} + 3616 q^{46} + 2370 q^{48} - 16288 q^{49} + 240 q^{50} - 284 q^{51} - 2998 q^{52} + 742 q^{53} + 854 q^{54} - 24 q^{55} + 4184 q^{56} + 216 q^{57} - 1398 q^{58} - 24 q^{59} - 2378 q^{60} - 14 q^{61} - 14 q^{62} + 216 q^{63} - 1256 q^{64} - 20 q^{65} - 3244 q^{66} + 2026 q^{67} + 3568 q^{68} + 98 q^{69} - 9338 q^{70} - 28 q^{71} - 13730 q^{72} + 1776 q^{73} - 10 q^{74} + 8750 q^{76} - 14 q^{77} - 1918 q^{78} + 3600 q^{79} - 3982 q^{80} - 26264 q^{81} - 11480 q^{82} - 10 q^{83} - 1674 q^{84} - 1764 q^{85} + 4068 q^{86} - 24 q^{87} + 1536 q^{88} - 88 q^{89} + 1182 q^{90} - 1814 q^{91} + 846 q^{92} - 10586 q^{93} - 2350 q^{94} + 500 q^{95} + 94 q^{96} - 24 q^{97} + 8630 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(464, [\chi])\) into newform subspaces

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