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Properties

Label 464.4.j
Level $464$
Weight $4$
Character orbit 464.j
Rep. character $\chi_{464}(307,\cdot)$
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.j (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

\( 356 q - 4 q^{2} + 32 q^{6} - 8 q^{7} + 38 q^{8} - 3132 q^{9} + O(q^{10}) \) \( 356 q - 4 q^{2} + 32 q^{6} - 8 q^{7} + 38 q^{8} - 3132 q^{9} + 14 q^{10} - 44 q^{11} - 26 q^{12} + 52 q^{14} + 108 q^{15} + 296 q^{16} - 4 q^{17} + 178 q^{18} - 4 q^{20} - 32 q^{22} - 8 q^{23} - 4 q^{24} + 562 q^{26} - 420 q^{28} + 198 q^{29} + 528 q^{30} + 246 q^{32} + 180 q^{34} + 760 q^{36} + 12 q^{37} + 32 q^{38} - 604 q^{39} - 830 q^{40} + 1476 q^{42} - 812 q^{43} + 22 q^{44} - 504 q^{45} - 916 q^{46} - 62 q^{48} + 16260 q^{49} + 982 q^{50} + 108 q^{51} - 40 q^{52} - 756 q^{53} - 868 q^{54} - 4 q^{55} - 1224 q^{56} + 216 q^{57} + 2020 q^{58} - 4 q^{59} - 1306 q^{60} - 4 q^{61} + 216 q^{63} - 3132 q^{64} - 8 q^{65} + 1994 q^{66} + 2040 q^{67} + 2144 q^{68} - 224 q^{70} - 2276 q^{72} - 296 q^{73} - 4 q^{74} - 3700 q^{75} - 2444 q^{76} + 528 q^{77} + 1904 q^{78} - 600 q^{79} - 3968 q^{80} + 26236 q^{81} + 1456 q^{82} - 4 q^{83} + 704 q^{84} + 496 q^{85} - 4472 q^{86} - 4 q^{87} - 1564 q^{88} - 88 q^{89} + 3952 q^{90} - 1800 q^{91} + 860 q^{92} + 4380 q^{93} + 2336 q^{94} + 500 q^{95} + 108 q^{96} - 4 q^{97} - 804 q^{98} - 1012 q^{99} + O(q^{100}) \)

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.