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Properties

Label 425.4.j
Level $425$
Weight $4$
Character orbit 425.j
Rep. character $\chi_{425}(149,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Sturm bound $180$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 280 168 112
Cusp forms 256 160 96
Eisenstein series 24 8 16

Trace form

\( 160 q + 648 q^{4} + 52 q^{6} + O(q^{10}) \) \( 160 q + 648 q^{4} + 52 q^{6} - 44 q^{11} + 180 q^{14} + 2088 q^{16} - 440 q^{21} - 144 q^{24} + 492 q^{29} - 788 q^{31} + 2068 q^{34} - 624 q^{39} - 484 q^{41} - 1112 q^{44} - 44 q^{46} - 40 q^{51} - 596 q^{54} + 1000 q^{56} - 868 q^{61} + 3448 q^{64} - 1400 q^{69} + 404 q^{71} + 2888 q^{74} + 1988 q^{79} - 19752 q^{81} - 4968 q^{84} + 3120 q^{86} + 1576 q^{89} - 8512 q^{91} + 1564 q^{96} - 5864 q^{99} + O(q^{100}) \)

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

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