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Properties

Label 975.2.ce
Level $975$
Weight $2$
Character orbit 975.ce
Rep. character $\chi_{975}(44,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1088$
Newform subspaces $1$
Sturm bound $280$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.ce (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(280\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

Total New Old
Modular forms 1152 1152 0
Cusp forms 1088 1088 0
Eisenstein series 64 64 0

Trace form

\( 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9} + O(q^{10}) \) \( 1088 q - 20 q^{3} + 2 q^{6} - 12 q^{9} - 20 q^{13} - 34 q^{15} + 248 q^{16} - 24 q^{19} + 12 q^{21} - 40 q^{22} - 28 q^{24} - 20 q^{27} - 100 q^{28} - 12 q^{31} + 40 q^{33} - 4 q^{34} - 140 q^{37} + 6 q^{39} + 32 q^{40} - 20 q^{42} + 30 q^{45} + 12 q^{46} - 20 q^{48} - 20 q^{52} - 100 q^{54} - 48 q^{55} - 140 q^{58} - 86 q^{60} + 72 q^{61} + 70 q^{63} - 36 q^{66} - 20 q^{67} - 192 q^{70} - 50 q^{72} + 60 q^{73} - 112 q^{76} + 60 q^{78} - 24 q^{79} + 20 q^{81} - 168 q^{84} - 196 q^{85} - 20 q^{87} - 44 q^{91} - 192 q^{94} - 20 q^{97} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
975.2.ce.a 975.ce 975.be $1088$ $7.785$ None \(0\) \(-20\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$