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Properties

Label 945.2.m
Level $945$
Weight $2$
Character orbit 945.m
Rep. character $\chi_{945}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $2$
Sturm bound $288$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(10\)

Dimensions

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

Total New Old
Modular forms 312 96 216
Cusp forms 264 96 168
Eisenstein series 48 0 48

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 16 q^{10} + 40 q^{13} - 88 q^{16} + 8 q^{22} + 8 q^{25} + 104 q^{37} - 80 q^{40} - 40 q^{43} + 56 q^{46} - 144 q^{52} + 16 q^{55} - 8 q^{58} + 32 q^{61} + 48 q^{67} - 8 q^{70} - 16 q^{73} - 88 q^{76} + 16 q^{82} + 72 q^{85} - 144 q^{88} - 48 q^{97} + O(q^{100}) \)

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.m.a 945.m 15.e $48$ $7.546$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
945.2.m.b 945.m 15.e $48$ $7.546$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)