↑

Properties

Label 1205.2.r
Level $1205$
Weight $2$
Character orbit 1205.r
Rep. character $\chi_{1205}(211,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $328$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.r (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 496 328 168
Cusp forms 480 328 152
Eisenstein series 16 0 16

Trace form

\( 328 q + O(q^{10}) \) \( 328 q + 8 q^{10} - 40 q^{12} - 56 q^{14} - 16 q^{15} - 360 q^{16} - 8 q^{17} + 8 q^{19} + 8 q^{21} + 48 q^{22} - 16 q^{23} + 8 q^{26} + 48 q^{27} + 128 q^{28} - 16 q^{29} - 8 q^{30} + 48 q^{31} - 40 q^{33} - 80 q^{34} - 296 q^{36} - 48 q^{39} + 8 q^{41} - 48 q^{42} - 40 q^{43} - 48 q^{44} + 24 q^{46} - 16 q^{47} - 160 q^{48} - 24 q^{49} + 112 q^{51} + 64 q^{52} + 56 q^{56} + 32 q^{57} + 16 q^{58} - 16 q^{59} + 48 q^{61} - 56 q^{62} + 88 q^{63} + 8 q^{65} + 8 q^{67} + 40 q^{68} - 32 q^{69} - 24 q^{70} + 8 q^{71} + 104 q^{73} + 32 q^{74} + 112 q^{76} + 64 q^{78} + 8 q^{79} - 32 q^{80} - 248 q^{81} - 40 q^{84} - 80 q^{86} - 176 q^{87} - 72 q^{88} - 88 q^{89} - 96 q^{91} + 128 q^{92} + 8 q^{93} - 16 q^{94} + 104 q^{98} + 56 q^{99} + O(q^{100}) \)

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

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