↑

Properties

Label 1205.2.br
Level $1205$
Weight $2$
Character orbit 1205.br
Rep. character $\chi_{1205}(81,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 976 640 336
Cusp forms 944 640 304
Eisenstein series 32 0 32

Trace form

\( 640 q + 8 q^{2} - 6 q^{3} - 314 q^{4} + 4 q^{5} - 6 q^{6} - 48 q^{8} + 88 q^{9} + O(q^{10}) \) \( 640 q + 8 q^{2} - 6 q^{3} - 314 q^{4} + 4 q^{5} - 6 q^{6} - 48 q^{8} + 88 q^{9} + 14 q^{10} + 4 q^{12} - 2 q^{13} - 30 q^{14} - 16 q^{15} - 302 q^{16} - 72 q^{19} - 6 q^{20} + 40 q^{21} + 18 q^{22} - 40 q^{24} - 160 q^{25} + 12 q^{27} - 20 q^{29} - 28 q^{30} - 34 q^{31} + 66 q^{32} + 110 q^{33} + 54 q^{34} + 10 q^{35} - 328 q^{36} + 28 q^{37} - 24 q^{38} - 6 q^{39} + 32 q^{40} - 54 q^{41} - 44 q^{42} + 30 q^{43} - 60 q^{45} - 20 q^{46} - 6 q^{47} - 120 q^{48} - 136 q^{49} - 2 q^{50} + 68 q^{51} - 104 q^{52} + 12 q^{53} + 24 q^{54} - 20 q^{55} + 28 q^{56} - 210 q^{57} - 98 q^{58} - 44 q^{59} - 34 q^{60} + 10 q^{61} + 106 q^{62} + 252 q^{63} + 640 q^{64} - 72 q^{65} + 88 q^{66} - 44 q^{67} - 52 q^{68} + 54 q^{69} + 30 q^{70} - 50 q^{71} - 10 q^{72} + 20 q^{73} - 16 q^{74} - 6 q^{75} - 6 q^{77} + 32 q^{78} - 8 q^{79} + 58 q^{80} - 18 q^{81} - 70 q^{82} + 18 q^{83} - 186 q^{84} - 80 q^{85} + 66 q^{86} - 88 q^{87} - 66 q^{88} + 6 q^{89} + 76 q^{90} + 132 q^{91} - 108 q^{92} + 26 q^{94} + 90 q^{96} + 188 q^{97} - 8 q^{98} + 260 q^{99} + O(q^{100}) \)

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

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