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Properties

Label 1205.2.cq
Level $1205$
Weight $2$
Character orbit 1205.cq
Rep. character $\chi_{1205}(52,\cdot)$
Character field $\Q(\zeta_{240})$
Dimension $7616$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.cq (of order \(240\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{240})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1205, [\chi])\).

Total New Old
Modular forms 7872 7872 0
Cusp forms 7616 7616 0
Eisenstein series 256 256 0

Trace form

\( 7616 q - 64 q^{2} - 64 q^{3} + 16 q^{4} - 64 q^{5} - 128 q^{6} - 96 q^{7} - 16 q^{9} + O(q^{10}) \) \( 7616 q - 64 q^{2} - 64 q^{3} + 16 q^{4} - 64 q^{5} - 128 q^{6} - 96 q^{7} - 16 q^{9} - 56 q^{10} - 128 q^{11} - 192 q^{12} - 64 q^{13} + 80 q^{14} - 32 q^{15} - 240 q^{16} - 16 q^{17} - 32 q^{18} - 64 q^{20} - 112 q^{21} - 64 q^{22} - 64 q^{23} - 16 q^{25} - 144 q^{26} - 40 q^{27} + 64 q^{28} - 144 q^{30} - 96 q^{31} - 176 q^{32} + 32 q^{33} - 24 q^{34} - 192 q^{35} - 160 q^{36} - 120 q^{37} - 168 q^{38} + 32 q^{40} - 96 q^{41} - 64 q^{43} + 48 q^{44} - 64 q^{45} + 96 q^{46} - 64 q^{47} + 80 q^{48} - 32 q^{49} + 752 q^{50} - 96 q^{51} - 160 q^{52} - 160 q^{53} - 64 q^{55} - 128 q^{56} - 192 q^{57} - 224 q^{58} - 144 q^{60} - 80 q^{61} - 128 q^{62} - 8 q^{63} - 192 q^{64} - 8 q^{65} - 128 q^{66} - 64 q^{67} - 80 q^{68} - 320 q^{69} - 64 q^{70} - 144 q^{71} - 152 q^{72} - 96 q^{73} - 16 q^{75} + 112 q^{76} + 256 q^{77} - 432 q^{78} + 16 q^{79} - 256 q^{80} - 448 q^{81} - 56 q^{82} - 128 q^{83} + 240 q^{84} - 16 q^{85} - 176 q^{86} - 48 q^{87} + 368 q^{88} - 160 q^{89} - 120 q^{90} - 96 q^{91} - 280 q^{92} - 72 q^{93} - 96 q^{95} - 448 q^{96} + 168 q^{97} - 48 q^{98} + 640 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1205, [\chi])\) into newform subspaces

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