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Properties

Label 425.4.k
Level $425$
Weight $4$
Character orbit 425.k
Rep. character $\chi_{425}(86,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $480$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 552 480 72
Cusp forms 536 480 56
Eisenstein series 16 0 16

Trace form

\( 480 q + 8 q^{3} - 480 q^{4} + 32 q^{5} + 24 q^{6} + 24 q^{7} - 126 q^{8} - 1144 q^{9} + O(q^{10}) \) \( 480 q + 8 q^{3} - 480 q^{4} + 32 q^{5} + 24 q^{6} + 24 q^{7} - 126 q^{8} - 1144 q^{9} + 54 q^{10} + 88 q^{11} - 144 q^{12} + 48 q^{13} - 20 q^{14} - 500 q^{15} - 1704 q^{16} + 508 q^{18} + 36 q^{19} + 42 q^{20} - 1158 q^{22} - 704 q^{23} - 1180 q^{24} - 68 q^{25} + 20 q^{26} - 916 q^{27} - 1068 q^{28} + 300 q^{29} - 344 q^{30} + 1272 q^{31} + 792 q^{32} - 688 q^{33} + 136 q^{34} + 760 q^{35} - 5674 q^{36} + 192 q^{37} + 3524 q^{38} + 2368 q^{39} - 772 q^{40} + 368 q^{41} + 3970 q^{42} + 24 q^{43} + 880 q^{44} - 628 q^{45} + 1208 q^{46} - 3016 q^{47} - 3580 q^{48} + 22296 q^{49} - 5574 q^{50} - 1632 q^{51} - 3606 q^{52} + 1560 q^{53} - 240 q^{54} - 2072 q^{55} + 4044 q^{56} + 3440 q^{57} - 2760 q^{58} + 1896 q^{59} + 18900 q^{60} + 732 q^{61} + 1558 q^{62} + 5796 q^{63} - 1182 q^{64} - 320 q^{65} - 3632 q^{66} + 4656 q^{67} - 3904 q^{69} + 340 q^{70} + 3924 q^{71} - 12938 q^{72} - 3048 q^{73} - 10148 q^{74} - 5584 q^{75} - 304 q^{76} - 6200 q^{77} + 3388 q^{78} - 260 q^{79} - 18864 q^{80} - 3328 q^{81} + 10756 q^{82} + 3200 q^{83} + 4484 q^{84} - 408 q^{85} - 3116 q^{86} + 1976 q^{87} + 21256 q^{88} + 4240 q^{89} - 1756 q^{90} - 152 q^{91} + 12346 q^{92} - 800 q^{93} - 6624 q^{94} - 7284 q^{95} + 10764 q^{96} - 12828 q^{97} - 7202 q^{98} - 7616 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)