Properties

Label 825.6.bo
Level $825$
Weight $6$
Character orbit 825.bo
Rep. character $\chi_{825}(134,\cdot)$
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.bo (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

\( 2384 q - 10 q^{3} + 9470 q^{4} - 190 q^{7} - 94 q^{9} + O(q^{10}) \) \( 2384 q - 10 q^{3} + 9470 q^{4} - 190 q^{7} - 94 q^{9} + 1420 q^{10} - 490 q^{12} - 10 q^{13} + 1018 q^{15} - 148166 q^{16} - 10 q^{19} - 11710 q^{22} + 5110 q^{24} - 2134 q^{25} + 7175 q^{27} + 9110 q^{28} - 5 q^{30} + 9978 q^{31} + 25985 q^{33} + 52 q^{34} - 10246 q^{36} + 18255 q^{39} - 31260 q^{40} + 41145 q^{42} - 134400 q^{43} + 51163 q^{45} + 5115 q^{48} - 1338822 q^{49} + 1205 q^{51} + 20460 q^{52} - 98520 q^{54} + 215274 q^{55} - 191790 q^{58} + 313524 q^{60} - 4590 q^{61} + 84030 q^{63} + 2285606 q^{64} - 110055 q^{66} + 198710 q^{67} - 187349 q^{69} + 116094 q^{70} - 224930 q^{72} - 10 q^{73} + 61777 q^{75} - 2050 q^{78} + 79726 q^{81} + 320 q^{82} - 121860 q^{85} - 327690 q^{88} + 510355 q^{90} + 182840 q^{91} + 130155 q^{93} + 257225 q^{96} + 31858 q^{99} + O(q^{100}) \)

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

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