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Properties

Label 882.3.s
Level $882$
Weight $3$
Character orbit 882.s
Rep. character $\chi_{882}(557,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $9$
Sturm bound $504$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(504\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(882, [\chi])\).

Total New Old
Modular forms 736 56 680
Cusp forms 608 56 552
Eisenstein series 128 0 128

Trace form

\( 56 q + 56 q^{4} + O(q^{10}) \) \( 56 q + 56 q^{4} - 16 q^{10} - 56 q^{13} - 112 q^{16} + 20 q^{19} + 252 q^{25} + 100 q^{31} - 32 q^{34} - 196 q^{37} + 32 q^{40} - 280 q^{43} + 224 q^{46} - 56 q^{52} - 176 q^{55} - 224 q^{58} + 64 q^{61} - 448 q^{64} + 588 q^{67} - 60 q^{73} + 80 q^{76} - 364 q^{79} - 96 q^{82} - 448 q^{85} - 192 q^{94} - 480 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.3.s.a 882.s 21.h $4$ $24.033$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots\)
882.3.s.b 882.s 21.h $4$ $24.033$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots\)
882.3.s.c 882.s 21.h $4$ $24.033$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}-2\beta _{3}q^{8}+\cdots\)
882.3.s.d 882.s 21.h $4$ $24.033$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+2\beta _{3}q^{8}+\cdots\)
882.3.s.e 882.s 21.h $8$ $24.033$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{6})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
882.3.s.f 882.s 21.h $8$ $24.033$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}+2\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+\cdots\)
882.3.s.g 882.s 21.h $8$ $24.033$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}+2\zeta_{24}^{2}q^{4}-2\zeta_{24}q^{5}+\cdots\)
882.3.s.h 882.s 21.h $8$ $24.033$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{2}+2\beta _{1}q^{4}-\beta _{2}q^{5}+(-2\beta _{4}+\cdots)q^{8}+\cdots\)
882.3.s.i 882.s 21.h $8$ $24.033$ 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{6})q^{2}+2\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)