↑

Properties

Label 775.3.bi
Level $775$
Weight $3$
Character orbit 775.bi
Rep. character $\chi_{775}(118,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $376$
Sturm bound $240$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.bi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 664 392 272
Cusp forms 616 376 240
Eisenstein series 48 16 32

Trace form

\( 376 q + 8 q^{2} + 6 q^{3} - 28 q^{6} - 6 q^{7} - 36 q^{8} + O(q^{10}) \) \( 376 q + 8 q^{2} + 6 q^{3} - 28 q^{6} - 6 q^{7} - 36 q^{8} - 4 q^{11} + 24 q^{12} + 2 q^{13} - 1504 q^{16} + 2 q^{17} - 42 q^{18} + 8 q^{21} + 56 q^{22} - 20 q^{23} - 228 q^{26} + 420 q^{27} - 44 q^{28} - 148 q^{31} - 116 q^{32} - 68 q^{33} - 1044 q^{36} - 150 q^{37} + 126 q^{38} + 100 q^{41} - 190 q^{42} - 10 q^{43} + 448 q^{47} - 108 q^{48} + 76 q^{51} + 32 q^{52} - 30 q^{53} + 60 q^{56} + 82 q^{57} - 404 q^{58} - 248 q^{61} + 150 q^{62} + 388 q^{63} + 1328 q^{66} + 248 q^{67} + 248 q^{68} + 464 q^{71} - 1078 q^{72} - 342 q^{73} - 916 q^{76} - 424 q^{77} + 308 q^{78} + 1632 q^{81} + 124 q^{82} + 554 q^{83} + 300 q^{86} + 194 q^{87} - 522 q^{88} + 1400 q^{91} - 1460 q^{92} - 330 q^{93} + 2428 q^{96} + 276 q^{97} - 54 q^{98} + O(q^{100}) \)

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

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