Properties

Label 315.2.g
Level 315
Weight 2
Character orbit g
Rep. character \(\chi_{315}(314,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 96q^{46} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 80q^{64} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 64q^{79} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.g.a \(16\) \(2.515\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{14})q^{4}-\beta _{4}q^{5}-\beta _{12}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

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