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Properties

Label 1205.2.bb
Level $1205$
Weight $2$
Character orbit 1205.bb
Rep. character $\chi_{1205}(181,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 488 320 168
Cusp forms 472 320 152
Eisenstein series 16 0 16

Trace form

\( 320 q + 160 q^{4} + 16 q^{6} - 4 q^{7} + 184 q^{9} + O(q^{10}) \) \( 320 q + 160 q^{4} + 16 q^{6} - 4 q^{7} + 184 q^{9} - 4 q^{10} - 4 q^{11} - 20 q^{13} + 32 q^{14} - 8 q^{15} - 152 q^{16} - 28 q^{17} - 12 q^{19} - 4 q^{21} - 48 q^{22} + 20 q^{23} + 24 q^{24} - 320 q^{25} - 4 q^{26} + 24 q^{28} - 24 q^{29} + 32 q^{31} - 84 q^{33} - 64 q^{34} + 4 q^{35} + 448 q^{36} + 12 q^{37} + 44 q^{38} + 4 q^{39} - 24 q^{40} - 84 q^{42} - 8 q^{43} - 24 q^{44} - 16 q^{46} - 72 q^{49} - 36 q^{51} + 88 q^{52} + 8 q^{54} + 8 q^{55} + 40 q^{56} - 40 q^{57} - 8 q^{58} - 12 q^{59} + 20 q^{60} + 28 q^{62} - 48 q^{63} - 264 q^{64} + 8 q^{65} + 64 q^{66} + 48 q^{68} + 60 q^{69} - 12 q^{70} + 12 q^{71} + 32 q^{73} - 60 q^{74} - 120 q^{76} + 80 q^{78} + 48 q^{80} - 256 q^{81} + 52 q^{82} + 124 q^{83} - 128 q^{84} - 32 q^{85} + 72 q^{86} + 88 q^{87} - 196 q^{88} + 40 q^{89} + 20 q^{90} - 32 q^{91} + 72 q^{92} - 76 q^{93} - 36 q^{94} - 92 q^{96} - 20 q^{97} - 16 q^{98} + 44 q^{99} + O(q^{100}) \)

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.

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

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