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Properties

Label 825.2.cm
Level $825$
Weight $2$
Character orbit 825.cm
Rep. character $\chi_{825}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.cm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 992 480 512
Cusp forms 928 480 448
Eisenstein series 64 0 64

Trace form

\( 480 q + 12 q^{5} + 20 q^{7} + O(q^{10}) \) \( 480 q + 12 q^{5} + 20 q^{7} + 40 q^{10} - 16 q^{12} - 12 q^{15} + 120 q^{16} - 20 q^{17} + 40 q^{20} - 32 q^{22} - 48 q^{23} + 28 q^{25} - 60 q^{28} + 40 q^{30} - 16 q^{33} - 60 q^{35} - 480 q^{36} - 12 q^{37} - 84 q^{38} - 8 q^{42} + 100 q^{43} + 140 q^{44} + 48 q^{48} + 60 q^{49} - 24 q^{53} - 40 q^{55} + 144 q^{58} - 32 q^{60} - 80 q^{64} + 40 q^{65} + 32 q^{67} + 20 q^{69} + 8 q^{70} - 220 q^{74} - 40 q^{75} - 24 q^{77} + 24 q^{78} + 40 q^{79} + 120 q^{80} + 120 q^{81} - 48 q^{82} - 200 q^{85} - 20 q^{87} - 104 q^{88} + 120 q^{92} - 72 q^{93} - 80 q^{95} - 88 q^{97} + O(q^{100}) \)

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.cm.a 825.cm 275.ag $480$ $6.588$ None \(0\) \(0\) \(12\) \(20\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)