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Properties

Label 464.4.t
Level $464$
Weight $4$
Character orbit 464.t
Rep. character $\chi_{464}(75,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
Sturm bound $240$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 364 364 0
Cusp forms 356 356 0
Eisenstein series 8 8 0

Trace form

\( 356 q - 4 q^{3} - 32 q^{6} - 8 q^{7} - 42 q^{8} + 3132 q^{9} + O(q^{10}) \) \( 356 q - 4 q^{3} - 32 q^{6} - 8 q^{7} - 42 q^{8} + 3132 q^{9} - 18 q^{10} - 134 q^{12} + 52 q^{14} - 108 q^{15} + 296 q^{16} - 4 q^{17} - 34 q^{18} - 4 q^{19} - 4 q^{20} - 112 q^{21} + 32 q^{22} - 8 q^{23} - 4 q^{24} - 566 q^{26} - 376 q^{27} + 420 q^{28} - 202 q^{29} + 528 q^{30} - 250 q^{32} - 180 q^{34} + 760 q^{36} - 32 q^{38} - 604 q^{39} + 538 q^{40} - 1476 q^{42} + 1482 q^{44} - 504 q^{45} + 1620 q^{46} - 998 q^{48} + 16260 q^{49} - 254 q^{50} - 108 q^{51} - 40 q^{52} - 756 q^{53} - 868 q^{54} - 4 q^{55} + 1192 q^{56} - 216 q^{57} + 1384 q^{58} - 4 q^{59} - 4454 q^{60} - 216 q^{63} + 3132 q^{64} - 8 q^{65} + 3230 q^{66} - 2040 q^{67} + 1612 q^{68} - 112 q^{69} - 1764 q^{70} - 4540 q^{72} + 296 q^{73} - 4 q^{74} + 1736 q^{76} + 1904 q^{78} + 600 q^{79} + 3968 q^{80} + 26236 q^{81} + 1456 q^{82} - 4 q^{83} + 1660 q^{84} + 4472 q^{86} - 4 q^{87} - 1564 q^{88} + 88 q^{89} - 1196 q^{90} + 1800 q^{91} - 860 q^{92} - 4380 q^{93} + 2336 q^{94} - 500 q^{95} - 108 q^{96} - 4 q^{97} - 8644 q^{98} + O(q^{100}) \)

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.