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Properties

Label 425.4.s
Level $425$
Weight $4$
Character orbit 425.s
Rep. character $\chi_{425}(7,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $632$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.s (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 1128 664 464
Cusp forms 1032 632 400
Eisenstein series 96 32 64

Trace form

\( 632 q + 8 q^{2} + 8 q^{3} - 16 q^{6} + 8 q^{7} - 56 q^{8} + O(q^{10}) \) \( 632 q + 8 q^{2} + 8 q^{3} - 16 q^{6} + 8 q^{7} - 56 q^{8} - 16 q^{11} + 224 q^{12} + 832 q^{14} + 8 q^{17} + 16 q^{18} - 192 q^{19} - 16 q^{21} + 8 q^{22} + 8 q^{23} - 1488 q^{26} + 1112 q^{27} - 248 q^{28} + 1712 q^{31} + 456 q^{32} - 768 q^{33} + 1152 q^{34} + 3440 q^{36} + 872 q^{37} + 16 q^{38} - 2000 q^{39} + 904 q^{41} - 1112 q^{42} + 8 q^{43} - 3952 q^{46} + 3056 q^{47} - 5608 q^{48} - 16 q^{51} + 3088 q^{52} - 376 q^{53} - 3456 q^{54} - 16 q^{56} - 1208 q^{57} - 1280 q^{58} - 880 q^{59} - 16 q^{61} - 3928 q^{62} + 4736 q^{63} + 8448 q^{64} - 16 q^{66} + 192 q^{67} + 4528 q^{68} + 3120 q^{71} + 10112 q^{73} + 4880 q^{74} - 1552 q^{76} - 6728 q^{77} - 8880 q^{78} + 5440 q^{79} - 6928 q^{81} - 4328 q^{82} - 7496 q^{83} - 576 q^{84} - 5280 q^{86} - 7016 q^{87} - 8032 q^{88} - 4048 q^{91} + 1720 q^{92} + 6664 q^{93} - 8672 q^{94} + 9584 q^{96} + 8 q^{97} + 32640 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(425, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)