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Properties

Label 425.4.w
Level $425$
Weight $4$
Character orbit 425.w
Rep. character $\chi_{425}(4,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1056$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

Total New Old
Modular forms 1088 1088 0
Cusp forms 1056 1056 0
Eisenstein series 32 32 0

Trace form

\( 1056 q - 10 q^{3} - 1036 q^{4} - 30 q^{5} + 26 q^{6} + O(q^{10}) \) \( 1056 q - 10 q^{3} - 1036 q^{4} - 30 q^{5} + 26 q^{6} + 64 q^{10} + 78 q^{11} - 10 q^{12} - 20 q^{13} - 54 q^{14} - 3788 q^{16} - 10 q^{17} + 648 q^{20} - 444 q^{21} - 730 q^{22} + 270 q^{23} + 380 q^{24} - 670 q^{27} + 630 q^{28} + 550 q^{29} - 2092 q^{30} - 6 q^{31} - 980 q^{33} + 26 q^{34} + 1584 q^{35} + 3000 q^{37} - 20 q^{38} - 114 q^{39} + 1348 q^{40} - 602 q^{41} - 1412 q^{44} - 298 q^{45} + 1322 q^{46} - 3820 q^{47} + 6180 q^{48} + 636 q^{50} - 16 q^{51} + 140 q^{52} - 2938 q^{54} - 360 q^{55} - 1776 q^{56} - 1620 q^{58} + 542 q^{61} - 4930 q^{62} - 4340 q^{63} - 12908 q^{64} - 6264 q^{65} - 1460 q^{67} - 972 q^{69} - 3514 q^{71} + 1260 q^{72} + 7430 q^{73} + 1420 q^{74} - 2914 q^{75} + 5850 q^{78} + 1290 q^{79} - 356 q^{80} + 16188 q^{81} - 1164 q^{84} - 426 q^{85} - 2228 q^{86} - 780 q^{88} + 2724 q^{89} - 1654 q^{90} + 4140 q^{91} + 4290 q^{92} + 1658 q^{95} + 9528 q^{96} - 10 q^{97} - 13440 q^{98} - 520 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

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