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Properties

Label 775.3.cq
Level $775$
Weight $3$
Character orbit 775.cq
Rep. character $\chi_{775}(119,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1264$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.cq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 1296 1296 0
Cusp forms 1264 1264 0
Eisenstein series 32 32 0

Trace form

\( 1264 q - 20 q^{2} - 15 q^{3} + 612 q^{4} - 16 q^{5} - 33 q^{6} + 10 q^{8} + 479 q^{9} + O(q^{10}) \) \( 1264 q - 20 q^{2} - 15 q^{3} + 612 q^{4} - 16 q^{5} - 33 q^{6} + 10 q^{8} + 479 q^{9} - 33 q^{10} - 9 q^{11} - 15 q^{12} - 15 q^{13} - 21 q^{14} - 1260 q^{16} - 15 q^{17} - 3 q^{19} - 5 q^{20} - 9 q^{21} + 330 q^{22} - 6 q^{24} - 12 q^{25} + 102 q^{26} + 195 q^{28} - 36 q^{31} - 20 q^{33} - 33 q^{34} - 206 q^{35} - 1193 q^{36} - 15 q^{37} - 170 q^{38} - 48 q^{39} + 274 q^{40} + 42 q^{41} - 705 q^{42} + 63 q^{44} - 233 q^{45} + 210 q^{47} - 75 q^{48} + 3960 q^{49} - 604 q^{50} + 126 q^{51} + 330 q^{52} - 15 q^{53} + 411 q^{55} + 78 q^{56} - 78 q^{59} - 575 q^{62} - 510 q^{63} + 2738 q^{64} + 780 q^{65} + 964 q^{66} + 550 q^{67} - 305 q^{69} - 342 q^{70} + 67 q^{71} + 210 q^{72} + 45 q^{73} - 48 q^{74} - 264 q^{75} + 16 q^{76} - 2190 q^{78} - 9 q^{79} + 531 q^{80} + 883 q^{81} + 885 q^{83} + 63 q^{84} - 333 q^{86} + 520 q^{87} - 1455 q^{88} - 564 q^{90} + 356 q^{94} + 668 q^{95} - 354 q^{96} - 300 q^{97} - 515 q^{98} - 438 q^{99} + O(q^{100}) \)

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.