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Properties

Label 425.4.bd
Level $425$
Weight $4$
Character orbit 425.bd
Rep. character $\chi_{425}(9,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $2144$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.bd (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 2208 2208 0
Cusp forms 2144 2144 0
Eisenstein series 64 64 0

Trace form

\( 2144 q - 20 q^{2} - 20 q^{3} - 12 q^{6} - 20 q^{8} - 12 q^{9} + O(q^{10}) \) \( 2144 q - 20 q^{2} - 20 q^{3} - 12 q^{6} - 20 q^{8} - 12 q^{9} - 24 q^{10} + 156 q^{11} - 20 q^{12} - 12 q^{14} - 184 q^{15} + 8552 q^{16} - 20 q^{17} - 12 q^{19} - 1104 q^{20} - 20 q^{22} - 20 q^{23} - 544 q^{24} - 336 q^{25} + 176 q^{26} - 20 q^{27} - 1300 q^{28} - 604 q^{29} - 12 q^{31} + 1880 q^{33} - 12 q^{34} + 464 q^{35} - 428 q^{36} - 20 q^{37} + 204 q^{39} - 1428 q^{40} + 2100 q^{41} - 20 q^{42} - 524 q^{44} - 1648 q^{45} - 2604 q^{46} - 12240 q^{48} + 928 q^{49} - 1048 q^{50} - 32 q^{51} - 40 q^{52} + 940 q^{53} + 312 q^{54} - 524 q^{56} - 3240 q^{58} - 12 q^{59} - 2356 q^{60} + 1300 q^{61} - 9860 q^{62} - 20 q^{63} - 4284 q^{65} + 7304 q^{66} - 40 q^{67} + 6888 q^{69} + 908 q^{70} - 12 q^{71} - 5780 q^{73} + 3344 q^{74} + 3520 q^{75} - 480 q^{76} - 2260 q^{77} + 11160 q^{78} + 2580 q^{79} - 6188 q^{80} - 18780 q^{83} - 9112 q^{84} - 5104 q^{85} - 18024 q^{86} + 8180 q^{87} + 1520 q^{88} + 27156 q^{90} - 4704 q^{91} - 8620 q^{92} - 6900 q^{94} - 5936 q^{95} + 13276 q^{96} - 20 q^{97} + 4792 q^{99} + O(q^{100}) \)

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.