↑

Properties

Label 1210.2.g
Level $1210$
Weight $2$
Character orbit 1210.g
Rep. character $\chi_{1210}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $144$
Sturm bound $396$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1210.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1210, [\chi])\).

Total New Old
Modular forms 888 144 744
Cusp forms 696 144 552
Eisenstein series 192 0 192

Trace form

\( 144 q - 2 q^{2} - 4 q^{3} - 36 q^{4} + 6 q^{6} - 2 q^{8} - 28 q^{9} + O(q^{10}) \) \( 144 q - 2 q^{2} - 4 q^{3} - 36 q^{4} + 6 q^{6} - 2 q^{8} - 28 q^{9} + 8 q^{10} - 4 q^{12} + 8 q^{13} - 2 q^{14} + 12 q^{15} - 36 q^{16} - 8 q^{17} - 16 q^{18} + 14 q^{19} - 48 q^{21} + 6 q^{24} - 36 q^{25} + 12 q^{26} + 26 q^{27} + 40 q^{29} - 4 q^{30} + 8 q^{32} + 44 q^{34} - 8 q^{35} - 38 q^{36} + 8 q^{37} - 20 q^{38} + 32 q^{39} - 2 q^{40} + 30 q^{41} + 8 q^{42} - 12 q^{43} + 8 q^{46} - 36 q^{47} - 4 q^{48} - 86 q^{49} - 2 q^{50} - 10 q^{51} - 12 q^{52} - 8 q^{53} - 16 q^{54} - 12 q^{56} - 70 q^{57} - 40 q^{58} - 62 q^{59} - 8 q^{60} + 24 q^{61} - 4 q^{62} + 44 q^{63} - 36 q^{64} + 20 q^{65} + 44 q^{67} - 8 q^{68} + 12 q^{69} + 8 q^{71} + 14 q^{72} + 24 q^{73} + 4 q^{74} + 6 q^{75} - 16 q^{76} + 96 q^{78} - 58 q^{81} + 10 q^{82} + 34 q^{83} + 12 q^{84} - 28 q^{85} - 42 q^{86} + 48 q^{87} - 26 q^{90} + 94 q^{91} + 20 q^{92} + 144 q^{93} + 26 q^{94} - 4 q^{96} + 142 q^{97} + 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1210, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)