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Properties

Label 400.4.j
Level $400$
Weight $4$
Character orbit 400.j
Rep. character $\chi_{400}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 400.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

Total New Old
Modular forms 372 220 152
Cusp forms 348 212 136
Eisenstein series 24 8 16

Trace form

\( 212 q + 2 q^{2} - 24 q^{4} - 4 q^{6} + 4 q^{7} - 40 q^{8} - 1836 q^{9} + O(q^{10}) \) \( 212 q + 2 q^{2} - 24 q^{4} - 4 q^{6} + 4 q^{7} - 40 q^{8} - 1836 q^{9} - 4 q^{11} - 28 q^{12} + 4 q^{13} + 260 q^{16} + 4 q^{17} + 202 q^{18} + 48 q^{19} - 4 q^{21} - 360 q^{22} + 4 q^{23} + 108 q^{24} - 548 q^{26} - 240 q^{28} - 628 q^{32} + 4 q^{33} - 304 q^{34} + 604 q^{36} + 4 q^{37} - 564 q^{38} + 916 q^{42} - 860 q^{43} - 1700 q^{44} - 100 q^{46} + 408 q^{47} - 380 q^{48} - 1492 q^{51} - 1640 q^{52} + 2284 q^{54} - 88 q^{56} - 108 q^{57} - 2068 q^{58} - 1376 q^{59} + 1820 q^{61} + 2412 q^{62} - 108 q^{63} + 1824 q^{64} + 6028 q^{66} - 1844 q^{67} + 1752 q^{68} + 1164 q^{69} + 440 q^{71} + 4112 q^{72} + 296 q^{73} + 1912 q^{74} - 5124 q^{76} - 1372 q^{78} + 14572 q^{81} - 2548 q^{82} - 6012 q^{84} + 2060 q^{86} + 1292 q^{87} - 1120 q^{88} - 1700 q^{91} + 3304 q^{92} - 104 q^{93} - 3432 q^{94} + 2788 q^{96} + 4 q^{97} + 4746 q^{98} - 5204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(400, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)