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Properties

Label 975.2.cf
Level $975$
Weight $2$
Character orbit 975.cf
Rep. character $\chi_{975}(53,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
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.cf (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
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 960 192
Cusp forms 1088 960 128
Eisenstein series 64 0 64

Trace form

\( 960 q + 4 q^{3} + 8 q^{7} + O(q^{10}) \) \( 960 q + 4 q^{3} + 8 q^{7} - 16 q^{12} + 4 q^{15} + 240 q^{16} + 28 q^{18} - 80 q^{22} - 112 q^{25} + 16 q^{27} - 128 q^{28} - 28 q^{30} - 4 q^{33} - 40 q^{37} - 8 q^{40} - 180 q^{42} - 16 q^{43} - 116 q^{45} - 68 q^{48} + 8 q^{52} - 140 q^{57} + 88 q^{58} - 156 q^{60} - 48 q^{63} + 80 q^{64} + 88 q^{67} + 120 q^{70} + 244 q^{72} + 72 q^{73} + 92 q^{75} + 80 q^{79} - 40 q^{81} - 128 q^{82} + 240 q^{84} + 80 q^{85} + 20 q^{87} + 32 q^{88} + 40 q^{90} + 40 q^{93} - 280 q^{94} - 184 q^{97} + O(q^{100}) \)

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.cf.a 975.cf 75.l $960$ $7.785$ None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)