Properties

Label 5184.2.f
Level $5184$
Weight $2$
Character orbit 5184.f
Rep. character $\chi_{5184}(2591,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $6$
Sturm bound $1728$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1728\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5184, [\chi])\).

Total New Old
Modular forms 936 96 840
Cusp forms 792 96 696
Eisenstein series 144 0 144

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 96 q^{25} - 96 q^{49} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5184, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5184.2.f.a 5184.f 24.f $16$ $41.394$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{5}+(\beta _{10}+\beta _{11})q^{7}+(-\beta _{7}+\cdots)q^{11}+\cdots\)
5184.2.f.b 5184.f 24.f $16$ $41.394$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(\beta _{9}+\beta _{11})q^{7}+\beta _{14}q^{11}+\cdots\)
5184.2.f.c 5184.f 24.f $16$ $41.394$ 16.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{5}-\beta _{12}q^{7}+\beta _{1}q^{11}-\beta _{7}q^{13}+\cdots\)
5184.2.f.d 5184.f 24.f $16$ $41.394$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}-\beta _{1}q^{7}+\beta _{11}q^{11}+\beta _{7}q^{13}+\cdots\)
5184.2.f.e 5184.f 24.f $16$ $41.394$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(\beta _{9}+\beta _{11})q^{7}+\beta _{14}q^{11}+\cdots\)
5184.2.f.f 5184.f 24.f $16$ $41.394$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{5}+(-\beta _{10}-\beta _{11})q^{7}+(-\beta _{7}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5184, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5184, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2592, [\chi])\)\(^{\oplus 2}\)