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Properties

Label 825.2.cy
Level $825$
Weight $2$
Character orbit 825.cy
Rep. character $\chi_{825}(172,\cdot)$
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.cy (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

\( 480 q - 8 q^{5} + O(q^{10}) \) \( 480 q - 8 q^{5} - 40 q^{10} - 16 q^{12} - 20 q^{13} + 8 q^{15} + 120 q^{16} - 20 q^{17} + 20 q^{19} - 60 q^{20} - 52 q^{22} - 48 q^{23} + 8 q^{25} - 140 q^{28} + 44 q^{33} + 120 q^{36} + 8 q^{37} + 56 q^{38} + 12 q^{42} - 100 q^{43} + 20 q^{47} - 32 q^{48} - 60 q^{49} - 80 q^{50} + 40 q^{52} - 24 q^{53} + 40 q^{55} - 80 q^{57} + 44 q^{58} + 60 q^{59} + 48 q^{60} + 120 q^{62} - 40 q^{63} + 40 q^{64} - 40 q^{65} + 32 q^{67} + 220 q^{68} - 72 q^{70} - 60 q^{73} + 220 q^{74} + 276 q^{77} + 24 q^{78} - 280 q^{80} + 120 q^{81} + 32 q^{82} + 40 q^{85} + 20 q^{87} - 104 q^{88} + 20 q^{92} - 72 q^{93} - 180 q^{94} + 20 q^{95} - 128 q^{97} + O(q^{100}) \)

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.cy.a 825.cy 275.an $480$ $6.588$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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