Properties

Label 1205.2.f
Level $1205$
Weight $2$
Character orbit 1205.f
Rep. character $\chi_{1205}(546,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $164$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(i)\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 244 164 80
Cusp forms 236 164 72
Eisenstein series 8 0 8

Trace form

\( 164 q - 164 q^{4} + 8 q^{6} - 12 q^{7} - 188 q^{9} + O(q^{10}) \) \( 164 q - 164 q^{4} + 8 q^{6} - 12 q^{7} - 188 q^{9} + 4 q^{10} - 8 q^{11} - 20 q^{13} + 28 q^{14} + 8 q^{15} + 180 q^{16} - 8 q^{17} - 16 q^{19} - 36 q^{21} + 12 q^{22} + 16 q^{23} - 24 q^{24} - 164 q^{25} + 4 q^{26} + 64 q^{28} + 32 q^{31} + 48 q^{33} + 16 q^{34} - 4 q^{35} + 204 q^{36} - 40 q^{37} - 44 q^{38} + 12 q^{39} - 12 q^{40} - 36 q^{42} + 36 q^{43} + 24 q^{44} - 20 q^{46} + 36 q^{51} + 48 q^{52} - 80 q^{54} - 8 q^{55} - 76 q^{56} - 36 q^{57} + 8 q^{58} - 8 q^{60} - 28 q^{62} - 8 q^{63} - 124 q^{64} - 8 q^{65} - 88 q^{66} + 36 q^{68} + 12 q^{69} + 12 q^{70} - 12 q^{71} + 8 q^{73} + 12 q^{74} + 88 q^{76} - 56 q^{78} + 356 q^{81} + 56 q^{82} - 136 q^{83} + 48 q^{84} - 16 q^{85} + 24 q^{86} + 56 q^{87} - 44 q^{88} + 56 q^{89} - 20 q^{90} + 40 q^{91} - 48 q^{93} - 16 q^{96} - 88 q^{97} + 124 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(241, [\chi])\)\(^{\oplus 2}\)