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Properties

Label 5292.2.l
Level $5292$
Weight $2$
Character orbit 5292.l
Rep. character $\chi_{5292}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $10$
Sturm bound $2016$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(2016\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5292, [\chi])\).

Total New Old
Modular forms 2160 80 2080
Cusp forms 1872 80 1792
Eisenstein series 288 0 288

Trace form

\( 80 q + 8 q^{5} + O(q^{10}) \) \( 80 q + 8 q^{5} + 8 q^{11} + q^{13} - 5 q^{17} - 2 q^{19} - 22 q^{23} + 80 q^{25} + 6 q^{29} - 2 q^{31} + q^{37} - 24 q^{41} - 2 q^{43} - 6 q^{47} - 22 q^{53} + 12 q^{55} - 7 q^{59} + 13 q^{61} + 11 q^{65} + 7 q^{67} - 38 q^{71} - 14 q^{73} + 7 q^{79} - 26 q^{83} + 12 q^{85} - 21 q^{89} - 54 q^{95} + q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(5292, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5292.2.l.a 5292.l 63.g $2$ $42.257$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-3q^{5}-3q^{11}+(1-\zeta_{6})q^{13}+(6-6\zeta_{6})q^{17}+\cdots\)
5292.2.l.b 5292.l 63.g $2$ $42.257$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2q^{5}-4q^{11}+(3-3\zeta_{6})q^{13}+(-7+\cdots)q^{17}+\cdots\)
5292.2.l.c 5292.l 63.g $2$ $42.257$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+3q^{5}-3q^{11}+(-1+\zeta_{6})q^{13}+(-6+\cdots)q^{17}+\cdots\)
5292.2.l.d 5292.l 63.g $6$ $42.257$ 6.0.309123.1 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}+\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
5292.2.l.e 5292.l 63.g $6$ $42.257$ 6.0.309123.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(-1+\beta _{1}-2\beta _{3})q^{11}+(-1+\cdots)q^{13}+\cdots\)
5292.2.l.f 5292.l 63.g $6$ $42.257$ 6.0.309123.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{5}+(-1+\beta _{1}-2\beta _{3})q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
5292.2.l.g 5292.l 63.g $6$ $42.257$ 6.0.309123.1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots\)
5292.2.l.h 5292.l 63.g $12$ $42.257$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{6}+\beta _{8})q^{5}+(1+\beta _{7})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
5292.2.l.i 5292.l 63.g $14$ $42.257$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{4})q^{5}-\beta _{13}q^{11}-\beta _{11}q^{13}+\cdots\)
5292.2.l.j 5292.l 63.g $24$ $42.257$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5292, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5292, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2646, [\chi])\)\(^{\oplus 2}\)