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Properties

Label 464.4.bj
Level $464$
Weight $4$
Character orbit 464.bj
Rep. character $\chi_{464}(5,\cdot)$
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.bj (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

\( 2136 q - 14 q^{2} - 14 q^{3} - 30 q^{4} - 10 q^{5} - 70 q^{6} - 14 q^{8} + O(q^{10}) \) \( 2136 q - 14 q^{2} - 14 q^{3} - 30 q^{4} - 10 q^{5} - 70 q^{6} - 14 q^{8} - 14 q^{10} - 154 q^{11} - 10 q^{13} - 14 q^{14} - 28 q^{15} - 310 q^{16} - 14 q^{18} - 14 q^{19} - 318 q^{20} - 14 q^{21} + 328 q^{22} - 10 q^{24} - 14 q^{26} - 14 q^{27} + 316 q^{28} - 212 q^{29} - 588 q^{30} - 28 q^{31} - 14 q^{32} - 20 q^{33} - 218 q^{34} - 510 q^{35} + 754 q^{36} - 14 q^{37} + 4256 q^{38} - 14 q^{40} - 874 q^{42} - 14 q^{43} - 1764 q^{44} - 618 q^{45} - 28 q^{47} + 3682 q^{48} + 16248 q^{49} - 14 q^{50} + 260 q^{51} + 6848 q^{52} + 742 q^{53} - 654 q^{54} - 6090 q^{56} - 3410 q^{58} + 2016 q^{59} + 8554 q^{60} - 14 q^{61} - 1664 q^{62} - 5284 q^{63} + 1188 q^{64} - 996 q^{65} - 9590 q^{66} + 2030 q^{67} - 4312 q^{68} - 14 q^{69} + 10696 q^{72} - 1326 q^{74} - 14 q^{76} - 14 q^{77} - 890 q^{78} - 28 q^{79} + 1420 q^{80} + 26224 q^{81} - 2426 q^{82} - 10 q^{83} - 4816 q^{84} + 1736 q^{85} + 3880 q^{86} + 2436 q^{88} - 16394 q^{90} + 418 q^{91} + 3052 q^{92} + 10562 q^{93} + 11052 q^{94} - 28 q^{95} - 1586 q^{96} - 28 q^{97} - 14 q^{98} + O(q^{100}) \)

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.