↑

Properties

Label 825.2.br
Level $825$
Weight $2$
Character orbit 825.br
Rep. character $\chi_{825}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $464$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.br (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

\( 464 q - 5 q^{3} + 110 q^{4} - 5 q^{6} - 10 q^{7} + q^{9} + O(q^{10}) \) \( 464 q - 5 q^{3} + 110 q^{4} - 5 q^{6} - 10 q^{7} + q^{9} - 20 q^{10} - 40 q^{12} - 10 q^{13} + 3 q^{15} - 106 q^{16} - 20 q^{19} + 10 q^{24} + 16 q^{25} - 5 q^{27} - 80 q^{28} - 45 q^{30} - 12 q^{31} + 20 q^{33} - 8 q^{34} + 29 q^{36} - 10 q^{37} + 35 q^{39} - 10 q^{40} - 47 q^{45} + 10 q^{46} - 142 q^{49} + 5 q^{51} - 10 q^{52} - 30 q^{54} - 16 q^{55} + 10 q^{58} - 26 q^{60} - 10 q^{61} - 10 q^{63} + 126 q^{64} + 55 q^{66} - 90 q^{67} - 9 q^{69} - 76 q^{70} - 90 q^{72} - 20 q^{73} + 72 q^{75} + 50 q^{78} - 10 q^{79} + q^{81} - 20 q^{82} + 50 q^{85} - 50 q^{88} + 90 q^{90} + 60 q^{91} + 45 q^{93} + 130 q^{94} - 65 q^{96} - 110 q^{97} - 62 q^{99} + O(q^{100}) \)

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.br.a 825.br 825.ar $464$ $6.588$ None \(0\) \(-5\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$