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Properties

Label 825.6.bf
Level $825$
Weight $6$
Character orbit 825.bf
Rep. character $\chi_{825}(266,\cdot)$
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.bf (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

\( 2384 q + 2 q^{3} - 9474 q^{4} - 210 q^{7} - 94 q^{9} + O(q^{10}) \) \( 2384 q + 2 q^{3} - 9474 q^{4} - 210 q^{7} - 94 q^{9} + 1420 q^{10} + 1126 q^{12} - 10 q^{13} + 888 q^{15} - 150846 q^{16} - 10 q^{18} - 10 q^{19} + 5718 q^{22} + 5110 q^{24} + 13838 q^{25} - 4309 q^{27} + 9750 q^{28} - 5 q^{30} - 9982 q^{31} - 2667 q^{33} - 76 q^{34} - 2054 q^{36} - 40788 q^{37} + 20685 q^{39} + 31240 q^{40} + 50033 q^{42} - 67551 q^{45} - 51701 q^{48} + 1407922 q^{49} - 1225 q^{51} - 98520 q^{54} - 173250 q^{55} + 287910 q^{57} - 161758 q^{58} - 3630 q^{60} + 4570 q^{61} + 84030 q^{63} - 2367578 q^{64} + 63393 q^{66} + 55774 q^{67} - 50213 q^{69} - 217774 q^{70} - 224610 q^{72} - 10 q^{73} + 88977 q^{75} - 105098 q^{78} + 8622 q^{81} - 538484 q^{82} + 121840 q^{85} - 225520 q^{87} - 859646 q^{88} + 1955 q^{90} - 182844 q^{91} + 254421 q^{93} - 246995 q^{96} - 536000 q^{97} + 31858 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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