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Properties

Label 1601.2.p
Level $1601$
Weight $2$
Character orbit 1601.p
Rep. character $\chi_{1601}(43,\cdot)$
Character field $\Q(\zeta_{160})$
Dimension $8512$
Sturm bound $267$

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Defining parameters

Level: \( N \) \(=\) \( 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1601.p (of order \(160\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1601 \)
Character field: \(\Q(\zeta_{160})\)
Sturm bound: \(267\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1601, [\chi])\).

Total New Old
Modular forms 8640 8640 0
Cusp forms 8512 8512 0
Eisenstein series 128 128 0

Trace form

\( 8512 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 80 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} + O(q^{10}) \) \( 8512 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 80 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 80 q^{16} - 64 q^{17} + 32 q^{18} - 112 q^{19} - 64 q^{20} - 64 q^{21} - 208 q^{22} - 64 q^{23} - 64 q^{24} - 128 q^{25} - 192 q^{26} - 64 q^{27} - 128 q^{28} - 80 q^{29} + 64 q^{30} - 80 q^{31} - 96 q^{32} + 48 q^{33} - 112 q^{34} + 64 q^{35} + 48 q^{36} - 192 q^{37} + 48 q^{38} - 64 q^{39} + 480 q^{42} - 112 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 144 q^{47} + 400 q^{48} - 64 q^{49} - 64 q^{50} - 48 q^{51} - 208 q^{52} - 80 q^{53} - 64 q^{54} - 64 q^{55} - 208 q^{56} + 304 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} + 48 q^{61} - 96 q^{62} - 144 q^{63} - 128 q^{64} - 144 q^{65} - 960 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 208 q^{73} - 64 q^{74} - 320 q^{75} - 80 q^{77} - 224 q^{78} - 144 q^{80} + 832 q^{81} + 128 q^{82} - 64 q^{83} + 960 q^{84} - 64 q^{85} + 112 q^{86} - 144 q^{87} - 224 q^{88} - 928 q^{89} - 368 q^{90} + 128 q^{91} - 320 q^{92} - 112 q^{93} - 64 q^{94} + 80 q^{95} - 416 q^{96} - 64 q^{97} - 64 q^{98} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1601, [\chi])\) into newform subspaces

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