Properties

Label 945.2.g
Level 945
Weight 2
Character orbit g
Rep. character \(\chi_{945}(944,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 2
Sturm bound 288
Trace bound 25

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 156 64 92
Cusp forms 132 64 68
Eisenstein series 24 0 24

Trace form

\(64q \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut +\mathstrut 112q^{64} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.g.a \(32\) \(7.546\) None \(0\) \(0\) \(0\) \(0\)
945.2.g.b \(32\) \(7.546\) None \(0\) \(0\) \(0\) \(0\)

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

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