Properties

Label 945.2.ca
Level 945
Weight 2
Character orbit ca
Rep. character \(\chi_{945}(368,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 176
Newforms 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.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 1 \)
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 624 208 416
Cusp forms 528 176 352
Eisenstein series 96 32 64

Trace form

\(176q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(176q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 68q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 90q^{32} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 36q^{40} \) \(\mathstrut +\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 36q^{50} \) \(\mathstrut -\mathstrut 52q^{52} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 96q^{56} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 78q^{65} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 72q^{92} \) \(\mathstrut +\mathstrut 66q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
945.2.ca.a \(176\) \(7.546\) None \(6\) \(0\) \(0\) \(-2\)

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

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