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Properties

Label 1604.2.w
Level $1604$
Weight $2$
Character orbit 1604.w
Rep. character $\chi_{1604}(119,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $6368$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 1604 = 2^{2} \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1604.w (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1604 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(402\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1604, [\chi])\).

Total New Old
Modular forms 6496 6496 0
Cusp forms 6368 6368 0
Eisenstein series 128 128 0

Trace form

\( 6368 q - 32 q^{2} - 32 q^{4} - 72 q^{5} - 32 q^{6} - 32 q^{8} - 64 q^{9} + O(q^{10}) \) \( 6368 q - 32 q^{2} - 32 q^{4} - 72 q^{5} - 32 q^{6} - 32 q^{8} - 64 q^{9} - 16 q^{10} - 64 q^{13} - 40 q^{14} - 40 q^{16} - 64 q^{17} - 32 q^{18} - 64 q^{21} - 32 q^{24} - 1696 q^{25} - 32 q^{26} + 8 q^{28} + 8 q^{30} - 72 q^{32} - 64 q^{33} - 32 q^{34} - 32 q^{36} + 8 q^{38} + 128 q^{40} - 80 q^{41} - 48 q^{42} + 168 q^{44} + 16 q^{45} - 128 q^{46} - 328 q^{48} - 96 q^{49} + 24 q^{50} - 224 q^{52} + 32 q^{53} - 72 q^{54} - 32 q^{56} - 64 q^{57} + 120 q^{60} - 104 q^{61} - 32 q^{62} - 32 q^{64} + 48 q^{65} - 32 q^{66} - 32 q^{68} - 64 q^{69} - 520 q^{70} - 64 q^{72} - 64 q^{73} - 32 q^{74} - 32 q^{76} - 48 q^{77} + 32 q^{78} + 720 q^{80} - 240 q^{81} - 48 q^{82} + 64 q^{84} + 16 q^{85} - 40 q^{86} - 24 q^{88} - 96 q^{89} + 160 q^{90} - 144 q^{92} - 64 q^{93} - 128 q^{94} - 168 q^{96} - 112 q^{97} - 128 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1604, [\chi])\) into newform subspaces

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