↑

Properties

Label 1205.2.cl
Level $1205$
Weight $2$
Character orbit 1205.cl
Rep. character $\chi_{1205}(17,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $3808$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.cl (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 3936 3936 0
Cusp forms 3808 3808 0
Eisenstein series 128 128 0

Trace form

\( 3808 q - 32 q^{2} - 32 q^{3} - 16 q^{4} - 32 q^{5} - 64 q^{6} - 48 q^{7} - 96 q^{8} + 16 q^{9} + O(q^{10}) \) \( 3808 q - 32 q^{2} - 32 q^{3} - 16 q^{4} - 32 q^{5} - 64 q^{6} - 48 q^{7} - 96 q^{8} + 16 q^{9} - 40 q^{10} - 64 q^{11} + 48 q^{12} - 32 q^{13} - 80 q^{14} - 64 q^{15} - 152 q^{17} + 8 q^{18} - 32 q^{20} - 80 q^{21} - 32 q^{22} - 32 q^{23} - 80 q^{25} - 48 q^{26} - 56 q^{27} - 160 q^{28} + 48 q^{30} - 96 q^{31} + 200 q^{32} + 16 q^{33} + 24 q^{34} - 96 q^{35} - 80 q^{36} + 24 q^{37} + 72 q^{38} - 128 q^{40} - 48 q^{41} - 32 q^{43} - 48 q^{44} - 32 q^{45} - 288 q^{46} - 32 q^{47} - 32 q^{48} + 32 q^{49} + 352 q^{50} - 96 q^{51} + 64 q^{52} - 80 q^{53} - 32 q^{55} - 64 q^{56} - 96 q^{57} - 40 q^{58} + 48 q^{60} - 112 q^{61} + 176 q^{62} + 80 q^{63} - 88 q^{65} - 64 q^{66} - 32 q^{67} - 16 q^{68} - 256 q^{69} - 32 q^{70} - 48 q^{71} - 496 q^{72} + 96 q^{73} - 8 q^{75} + 80 q^{76} - 352 q^{77} + 480 q^{78} - 16 q^{79} + 112 q^{80} - 80 q^{81} - 40 q^{82} - 136 q^{83} - 240 q^{84} - 8 q^{85} - 16 q^{86} - 24 q^{87} - 224 q^{88} + 160 q^{89} - 240 q^{90} - 48 q^{91} + 184 q^{92} - 24 q^{93} + 256 q^{96} + 24 q^{97} - 24 q^{98} + 320 q^{99} + O(q^{100}) \)

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.