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Properties

Label 1205.2.bd
Level $1205$
Weight $2$
Character orbit 1205.bd
Rep. character $\chi_{1205}(352,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $952$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 984 984 0
Cusp forms 952 952 0
Eisenstein series 32 32 0

Trace form

\( 952 q - 8 q^{2} - 8 q^{3} + 16 q^{4} - 8 q^{5} - 16 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + O(q^{10}) \) \( 952 q - 8 q^{2} - 8 q^{3} + 16 q^{4} - 8 q^{5} - 16 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{12} - 8 q^{13} - 16 q^{15} - 8 q^{17} - 48 q^{18} - 8 q^{20} - 8 q^{22} - 8 q^{23} + 40 q^{25} - 32 q^{26} + 16 q^{27} - 40 q^{28} - 88 q^{30} + 16 q^{31} - 56 q^{33} - 24 q^{34} - 24 q^{35} - 64 q^{37} - 112 q^{38} + 88 q^{40} - 32 q^{41} - 40 q^{42} - 8 q^{43} + 48 q^{44} - 8 q^{45} - 32 q^{46} - 8 q^{47} - 48 q^{48} - 32 q^{49} - 72 q^{50} + 16 q^{51} + 56 q^{52} + 40 q^{53} - 8 q^{55} - 16 q^{56} + 56 q^{57} + 72 q^{60} + 112 q^{61} - 16 q^{62} - 120 q^{63} + 48 q^{65} - 16 q^{66} - 8 q^{67} - 184 q^{68} + 16 q^{69} - 8 q^{70} - 32 q^{71} + 216 q^{72} - 16 q^{73} - 32 q^{75} - 160 q^{76} - 168 q^{77} + 16 q^{79} + 48 q^{80} + 96 q^{83} + 240 q^{84} - 32 q^{85} - 64 q^{86} - 16 q^{87} + 24 q^{88} - 160 q^{89} - 40 q^{90} - 32 q^{91} - 64 q^{92} - 16 q^{93} - 40 q^{95} + 144 q^{96} - 304 q^{97} - 16 q^{98} + 80 q^{99} + O(q^{100}) \)

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.