Properties

Label 825.2.cu
Level $825$
Weight $2$
Character orbit 825.cu
Rep. character $\chi_{825}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $928$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

Total New Old
Modular forms 992 992 0
Cusp forms 928 928 0
Eisenstein series 64 64 0

Trace form

\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} + O(q^{10}) \) \( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 60 q^{10} + 2 q^{12} - 4 q^{13} - 14 q^{15} + 204 q^{16} - 38 q^{18} - 40 q^{19} - 12 q^{21} - 60 q^{22} - 40 q^{24} - 48 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 4 q^{31} - 12 q^{33} - 40 q^{34} + 6 q^{36} + 16 q^{37} - 28 q^{40} - 6 q^{42} - 40 q^{43} - 78 q^{45} - 4 q^{46} - 6 q^{48} + 20 q^{49} - 12 q^{51} - 108 q^{52} + 40 q^{54} + 68 q^{55} + 30 q^{57} - 28 q^{58} - 80 q^{60} - 24 q^{61} + 56 q^{63} - 220 q^{64} + 30 q^{66} - 92 q^{67} + 90 q^{69} - 80 q^{70} - 138 q^{72} - 80 q^{73} - 46 q^{75} + 32 q^{76} - 160 q^{79} + 8 q^{81} + 52 q^{82} - 70 q^{84} + 28 q^{85} - 66 q^{87} + 124 q^{88} + 206 q^{90} - 4 q^{91} - 68 q^{93} - 20 q^{94} + 4 q^{96} - 56 q^{97} - 170 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.2.cu.a 825.cu 825.bu $928$ $6.588$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$