↑

Properties

Label 775.3.n
Level $775$
Weight $3$
Character orbit 775.n
Rep. character $\chi_{775}(99,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $188$
Sturm bound $240$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(775, [\chi])\).

Total New Old
Modular forms 332 196 136
Cusp forms 308 188 120
Eisenstein series 24 8 16

Trace form

\( 188 q - 352 q^{4} - 66 q^{6} - 248 q^{9} + O(q^{10}) \) \( 188 q - 352 q^{4} - 66 q^{6} - 248 q^{9} - 6 q^{11} - 36 q^{14} + 736 q^{16} + 36 q^{19} + 12 q^{21} + 324 q^{24} + 120 q^{26} + 252 q^{31} + 282 q^{34} + 318 q^{36} - 92 q^{39} + 20 q^{41} - 138 q^{44} + 406 q^{49} + 172 q^{51} + 198 q^{56} + 144 q^{59} - 876 q^{64} - 1732 q^{66} - 564 q^{69} - 396 q^{71} - 438 q^{74} + 158 q^{76} - 1014 q^{79} - 390 q^{81} - 18 q^{84} - 750 q^{86} + 1148 q^{94} - 1212 q^{96} - 348 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(775, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)