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Properties

Label 825.2.cg
Level $825$
Weight $2$
Character orbit 825.cg
Rep. character $\chi_{825}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $464$
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.cg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 825 \)
Character field: \(\Q(\zeta_{10})\)
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 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q + 2 q^{3} + 436 q^{4} - 15 q^{6} - 30 q^{7} - 4 q^{9} + O(q^{10}) \) \( 464 q + 2 q^{3} + 436 q^{4} - 15 q^{6} - 30 q^{7} - 4 q^{9} - 10 q^{10} - 14 q^{12} - 30 q^{13} - 12 q^{15} + 404 q^{16} - 10 q^{18} + 15 q^{21} - 32 q^{22} - 40 q^{24} - 32 q^{25} + 11 q^{27} - 80 q^{28} - 15 q^{30} - 12 q^{31} - 12 q^{33} - 16 q^{34} - 19 q^{36} - 18 q^{37} - 5 q^{39} - 70 q^{40} - 47 q^{42} - 21 q^{45} - 30 q^{46} - 26 q^{48} + 82 q^{49} + 5 q^{51} - 150 q^{52} - 50 q^{54} - 50 q^{55} - 90 q^{57} - 68 q^{58} - 20 q^{60} + 10 q^{61} - 5 q^{63} + 292 q^{64} + 38 q^{66} + 34 q^{67} - 8 q^{69} + 26 q^{70} + 10 q^{72} - 10 q^{73} + 62 q^{75} - 23 q^{78} - 80 q^{79} - 8 q^{81} - 24 q^{82} - 50 q^{84} - 50 q^{85} - 30 q^{87} - 176 q^{88} - 15 q^{90} - 74 q^{91} - 19 q^{93} - 170 q^{94} - 100 q^{96} + 10 q^{97} + 23 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.cg.a 825.cg 825.bg $464$ $6.588$ None \(0\) \(2\) \(0\) \(-30\) $\mathrm{SU}(2)[C_{10}]$