Properties

Label 5184.2.d
Level $5184$
Weight $2$
Character orbit 5184.d
Rep. character $\chi_{5184}(2593,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $18$
Sturm bound $1728$
Trace bound $41$

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Defining parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1728\)
Trace bound: \(41\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\), \(23\), \(41\)

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.d.a 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}+(-3-\zeta_{12}^{3})q^{7}+(-3\zeta_{12}+\cdots)q^{11}+\cdots\)
5184.2.d.b 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}+(-3+\zeta_{12}^{3})q^{7}+(3\zeta_{12}+\cdots)q^{11}+\cdots\)
5184.2.d.c 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}-3\zeta_{12}q^{11}-\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.d 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.e 5184.d 8.b $4$ $41.394$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{11}+(-3+\beta _{3})q^{17}+(-\beta _{1}+\cdots)q^{19}+\cdots\)
5184.2.d.f 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{11}-3\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.g 5184.d 8.b $4$ $41.394$ \(\Q(i, \sqrt{15})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+\beta _{2}q^{7}+3\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots\)
5184.2.d.h 5184.d 8.b $4$ $41.394$ \(\Q(i, \sqrt{15})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}-\beta _{2}q^{7}-3\beta _{1}q^{11}+\beta _{3}q^{13}+\cdots\)
5184.2.d.i 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{11}-3\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.j 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}-3\zeta_{12}q^{11}+\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.k 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{13}+\cdots\)
5184.2.d.l 5184.d 8.b $4$ $41.394$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{11}+(3-\beta _{3})q^{17}+(\beta _{1}+\cdots)q^{19}+\cdots\)
5184.2.d.m 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}+(3-\zeta_{12}^{3})q^{7}+(-3\zeta_{12}+\cdots)q^{11}+\cdots\)
5184.2.d.n 5184.d 8.b $4$ $41.394$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}+(3+\zeta_{12}^{3})q^{7}+(3\zeta_{12}+\cdots)q^{11}+\cdots\)
5184.2.d.o 5184.d 8.b $8$ $41.394$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{6}q^{5}-\zeta_{24}^{3}q^{7}-\zeta_{24}^{5}q^{11}+\cdots\)
5184.2.d.p 5184.d 8.b $8$ $41.394$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{6}q^{5}+\zeta_{24}^{3}q^{7}+\zeta_{24}^{5}q^{11}+\cdots\)
5184.2.d.q 5184.d 8.b $12$ $41.394$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{5}-\beta _{4}q^{7}+(-\beta _{7}-\beta _{9})q^{11}+\cdots\)
5184.2.d.r 5184.d 8.b $12$ $41.394$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{5}+\beta _{4}q^{7}+(\beta _{7}+\beta _{9})q^{11}+\beta _{10}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(5184, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2592, [\chi])\)\(^{\oplus 2}\)