Properties

Label 576.2.l
Level 576
Weight 2
Character orbit l
Rep. character \(\chi_{576}(143,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 16
Newforms 1
Sturm bound 192
Trace bound 0

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Defining parameters

Level: \( N \) = \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 576.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 224 16 208
Cusp forms 160 16 144
Eisenstein series 64 0 64

Trace form

\(16q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 64q^{55} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.2.l.a \(16\) \(4.599\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)