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Properties

Label 1205.2.ca
Level $1205$
Weight $2$
Character orbit 1205.ca
Rep. character $\chi_{1205}(38,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1904$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.ca (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 1968 1968 0
Cusp forms 1904 1904 0
Eisenstein series 64 64 0

Trace form

\( 1904 q - 16 q^{2} - 16 q^{3} + 16 q^{4} - 16 q^{5} - 32 q^{6} - 48 q^{7} - 32 q^{8} - 16 q^{9} + O(q^{10}) \) \( 1904 q - 16 q^{2} - 16 q^{3} + 16 q^{4} - 16 q^{5} - 32 q^{6} - 48 q^{7} - 32 q^{8} - 16 q^{9} - 24 q^{10} - 32 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{15} + 64 q^{17} + 16 q^{18} - 16 q^{20} - 48 q^{21} - 16 q^{22} - 16 q^{23} + 32 q^{25} - 16 q^{26} + 8 q^{27} - 48 q^{28} + 64 q^{30} - 64 q^{31} + 80 q^{32} + 80 q^{33} - 24 q^{34} + 16 q^{35} - 80 q^{37} - 120 q^{38} + 24 q^{40} - 64 q^{41} - 272 q^{42} - 16 q^{43} + 48 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} + 8 q^{48} - 32 q^{49} - 72 q^{50} - 64 q^{51} - 72 q^{52} + 32 q^{53} - 16 q^{55} - 32 q^{56} - 144 q^{57} + 144 q^{58} - 96 q^{60} - 160 q^{61} + 40 q^{62} - 184 q^{63} - 192 q^{64} + 40 q^{65} - 32 q^{66} - 16 q^{67} - 16 q^{68} + 160 q^{69} - 16 q^{70} - 16 q^{71} - 328 q^{72} + 72 q^{73} + 32 q^{75} - 272 q^{76} + 80 q^{77} + 136 q^{78} + 16 q^{79} - 88 q^{80} + 288 q^{81} - 8 q^{82} + 144 q^{83} + 240 q^{84} - 208 q^{85} + 16 q^{86} - 32 q^{87} + 64 q^{88} - 160 q^{89} + 200 q^{90} - 64 q^{91} - 72 q^{92} - 24 q^{93} + 16 q^{95} - 192 q^{96} - 144 q^{97} - 32 q^{98} - 160 q^{99} + O(q^{100}) \)

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.