Properties

Label 825.6.cg
Level $825$
Weight $6$
Character orbit 825.cg
Rep. character $\chi_{825}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2384$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 825.cg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(825, [\chi])\).

Total New Old
Modular forms 2416 2416 0
Cusp forms 2384 2384 0
Eisenstein series 32 32 0

Trace form

\( 2384 q + 2 q^{3} + 37876 q^{4} - 165 q^{6} + 170 q^{7} - 94 q^{9} + O(q^{10}) \) \( 2384 q + 2 q^{3} + 37876 q^{4} - 165 q^{6} + 170 q^{7} - 94 q^{9} - 1560 q^{10} - 1304 q^{12} - 2630 q^{13} + 888 q^{15} + 589964 q^{16} - 10 q^{18} + 1215 q^{21} - 3062 q^{22} - 5290 q^{24} + 3608 q^{25} - 4309 q^{27} + 8470 q^{28} - 165 q^{30} + 12188 q^{31} - 18222 q^{33} - 76 q^{34} - 7009 q^{36} + 26582 q^{37} - 5 q^{39} - 101020 q^{40} - 42317 q^{42} + 2799 q^{45} - 34330 q^{46} - 40436 q^{48} + 1381962 q^{49} + 1205 q^{51} - 178250 q^{52} + 98200 q^{54} - 115330 q^{55} + 287910 q^{57} + 29372 q^{58} + 152860 q^{60} - 4590 q^{61} - 5 q^{63} + 9050332 q^{64} + 104438 q^{66} - 3406 q^{67} - 165308 q^{69} + 139556 q^{70} - 389090 q^{72} - 10 q^{73} + 209582 q^{75} + 66517 q^{78} + 522120 q^{79} + 53062 q^{81} - 538484 q^{82} - 55400 q^{84} + 292350 q^{85} - 2430 q^{87} - 709566 q^{88} - 165 q^{90} + 9846 q^{91} - 209359 q^{93} - 337870 q^{94} - 170500 q^{96} - 222650 q^{97} + 447143 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

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