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Properties

Label 1075.6.bd
Level $1075$
Weight $6$
Character orbit 1075.bd
Rep. character $\chi_{1075}(11,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $13152$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bd (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(660\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1075, [\chi])\).

Total New Old
Modular forms 13248 13248 0
Cusp forms 13152 13152 0
Eisenstein series 96 96 0

Trace form

\( 13152 q - 15 q^{2} - 15 q^{3} + 8721 q^{4} - 42 q^{5} - 164 q^{6} + 140 q^{7} - 143 q^{8} + 44049 q^{9} + O(q^{10}) \) \( 13152 q - 15 q^{2} - 15 q^{3} + 8721 q^{4} - 42 q^{5} - 164 q^{6} + 140 q^{7} - 143 q^{8} + 44049 q^{9} - 652 q^{10} - 489 q^{11} + 917 q^{12} + 2605 q^{13} - 495 q^{14} - 1496 q^{15} + 130953 q^{16} + 1131 q^{17} - 5326 q^{18} - 8171 q^{19} - 2714 q^{20} - 3660 q^{21} + 5441 q^{22} - 2139 q^{23} + 25872 q^{24} - 12316 q^{25} + 32280 q^{26} - 11091 q^{27} - 399 q^{28} + 11163 q^{29} + 66499 q^{30} - 15 q^{31} + 19836 q^{32} + 45549 q^{33} - 9391 q^{34} - 36300 q^{35} - 4235140 q^{36} - 36 q^{37} - 175829 q^{38} - 9743 q^{39} - 241944 q^{40} - 15 q^{41} - 377156 q^{42} + 394996 q^{43} - 15074 q^{44} + 320779 q^{45} + 11289 q^{46} + 42715 q^{47} + 128119 q^{48} + 30899348 q^{49} - 85250 q^{50} + 242208 q^{51} - 227173 q^{52} + 92023 q^{53} + 118189 q^{54} - 103398 q^{55} - 240540 q^{56} + 53568 q^{57} - 175241 q^{58} - 97443 q^{59} - 277924 q^{60} + 87043 q^{61} - 193219 q^{62} - 524232 q^{63} + 2795825 q^{64} - 110122 q^{65} - 90251 q^{66} - 342335 q^{67} + 547336 q^{68} - 147651 q^{69} - 548058 q^{70} - 291379 q^{71} + 42919 q^{72} - 463049 q^{73} - 171948 q^{74} + 80193 q^{75} - 104104 q^{76} - 511590 q^{77} - 528563 q^{78} - 5780 q^{79} - 136846 q^{80} + 3489465 q^{81} + 1617596 q^{82} - 242165 q^{83} - 179108 q^{84} + 1765708 q^{85} + 148636 q^{86} - 1580966 q^{87} - 881679 q^{88} - 97896 q^{89} + 1321923 q^{90} - 384616 q^{91} + 401682 q^{92} - 430148 q^{93} + 501277 q^{94} - 993010 q^{95} + 1669247 q^{96} - 705555 q^{97} - 18296 q^{98} - 653190 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1075, [\chi])\) into newform subspaces

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