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Properties

Label 945.2.cf
Level $945$
Weight $2$
Character orbit 945.cf
Rep. character $\chi_{945}(8,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 624 144 480
Cusp forms 528 144 384
Eisenstein series 96 0 96

Trace form

\( 144 q + O(q^{10}) \) \( 144 q + 12 q^{11} + 72 q^{16} + 48 q^{20} + 24 q^{23} - 12 q^{25} + 60 q^{32} - 24 q^{37} - 72 q^{38} - 48 q^{41} - 48 q^{46} - 12 q^{47} - 24 q^{55} + 72 q^{65} - 12 q^{67} - 24 q^{76} - 96 q^{82} - 120 q^{83} - 48 q^{85} + 144 q^{86} - 48 q^{88} + 24 q^{91} - 156 q^{92} - 120 q^{95} - 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.cf.a 945.cf 45.l $144$ $7.546$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)