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Properties

Label 75.13.h
Level $75$
Weight $13$
Character orbit 75.h
Rep. character $\chi_{75}(14,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
Sturm bound $130$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 75.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(130\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(75, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 5 q^{3} - 237574 q^{4} + 8189 q^{6} - 434563 q^{9} + O(q^{10}) \) \( 472 q - 5 q^{3} - 237574 q^{4} + 8189 q^{6} - 434563 q^{9} + 1102980 q^{10} - 6553605 q^{12} - 10 q^{13} - 5421555 q^{15} - 532255530 q^{16} + 68440314 q^{19} - 78561360 q^{21} + 264268790 q^{22} + 125353828 q^{24} - 1365138800 q^{25} - 799075205 q^{27} + 3113205750 q^{28} + 133304215 q^{30} + 213363714 q^{31} - 4881968005 q^{33} + 5098397578 q^{34} - 14333508729 q^{36} - 23520697210 q^{37} - 17154812405 q^{39} - 19441630220 q^{40} + 37737295925 q^{42} - 4629274365 q^{45} - 41935387802 q^{46} + 121248548250 q^{48} - 810483479288 q^{49} + 28873210794 q^{51} - 31433803800 q^{52} + 95763197204 q^{54} + 87477714710 q^{55} + 213172139690 q^{58} - 193318864090 q^{60} - 124453936806 q^{61} - 123090583200 q^{63} - 1014165858126 q^{64} - 75352781930 q^{66} - 342195638410 q^{67} - 308943236881 q^{69} + 901630394760 q^{70} - 1143693086725 q^{72} - 9583780810 q^{73} + 539991193115 q^{75} - 752064044288 q^{76} + 1326158598625 q^{78} + 623149458954 q^{79} - 498724632723 q^{81} + 760520457120 q^{84} - 461279410230 q^{85} + 2523807648995 q^{87} + 714764321090 q^{88} + 414763117220 q^{90} - 242216020800 q^{91} - 50920811912 q^{94} - 558485383048 q^{96} + 5589677263790 q^{97} - 1264627900410 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

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