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Properties

Label 775.3.bh
Level $775$
Weight $3$
Character orbit 775.bh
Rep. character $\chi_{775}(581,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $632$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.bh (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 648 648 0
Cusp forms 632 632 0
Eisenstein series 16 16 0

Trace form

\( 632 q - 6 q^{2} + 1242 q^{4} - 14 q^{5} - 20 q^{6} - 22 q^{7} - 24 q^{8} + 466 q^{9} + O(q^{10}) \) \( 632 q - 6 q^{2} + 1242 q^{4} - 14 q^{5} - 20 q^{6} - 22 q^{7} - 24 q^{8} + 466 q^{9} + 37 q^{10} - 5 q^{11} - 75 q^{12} - 50 q^{14} - 50 q^{15} + 2402 q^{16} - 46 q^{18} - q^{19} - 100 q^{20} - 50 q^{21} - 50 q^{22} + 5 q^{23} - 135 q^{24} - 18 q^{25} - 75 q^{27} - 163 q^{28} - 5 q^{29} - 20 q^{30} + 67 q^{31} - 502 q^{32} + 151 q^{33} - 155 q^{35} + 961 q^{36} + 115 q^{37} - 247 q^{38} + 53 q^{39} + 54 q^{40} - 16 q^{41} + 405 q^{42} + 80 q^{43} + 150 q^{44} - 192 q^{45} - 45 q^{46} + 240 q^{47} - 265 q^{48} - 1268 q^{49} - 49 q^{50} - 212 q^{51} - 115 q^{53} - 225 q^{54} - 130 q^{55} - 435 q^{56} - 325 q^{58} - 306 q^{59} - 270 q^{60} - 630 q^{62} + 78 q^{63} + 4392 q^{64} - 485 q^{65} - 280 q^{66} + 123 q^{67} + 533 q^{69} + 124 q^{70} - 211 q^{71} - 1010 q^{72} + 815 q^{73} - 305 q^{74} - 105 q^{75} + 424 q^{76} + 95 q^{77} + 344 q^{78} - 105 q^{79} - 1480 q^{80} - 1350 q^{81} - 153 q^{82} + 1290 q^{83} - 365 q^{84} + 140 q^{85} - 1055 q^{86} - 580 q^{87} - 1175 q^{88} + 70 q^{89} - 691 q^{90} + 465 q^{91} - 445 q^{92} + 670 q^{93} + 75 q^{94} + 141 q^{95} - 590 q^{96} + 218 q^{97} + 40 q^{98} + O(q^{100}) \)

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.