Properties

Label 882.3.n
Level $882$
Weight $3$
Character orbit 882.n
Rep. character $\chi_{882}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $11$
Sturm bound $504$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
Sturm bound: \(504\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(23\)

Dimensions

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

Total New Old
Modular forms 736 68 668
Cusp forms 608 68 540
Eisenstein series 128 0 128

Trace form

\( 68 q - 68 q^{4} + 6 q^{5} + O(q^{10}) \) \( 68 q - 68 q^{4} + 6 q^{5} + 24 q^{10} + 18 q^{11} - 136 q^{16} - 78 q^{17} - 66 q^{19} + 88 q^{22} + 82 q^{23} + 148 q^{25} + 120 q^{26} + 160 q^{29} - 18 q^{31} - 58 q^{37} + 12 q^{38} - 48 q^{40} + 80 q^{43} + 36 q^{44} + 36 q^{46} + 42 q^{47} - 304 q^{50} + 48 q^{52} + 30 q^{53} + 64 q^{58} - 102 q^{59} + 402 q^{61} + 544 q^{64} - 144 q^{65} + 210 q^{67} + 156 q^{68} + 400 q^{71} + 30 q^{73} + 264 q^{74} - 334 q^{79} - 24 q^{80} - 264 q^{82} + 60 q^{85} + 80 q^{86} - 88 q^{88} - 450 q^{89} - 328 q^{92} - 372 q^{94} - 190 q^{95} + O(q^{100}) \)

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.n.a 882.n 7.d $4$ $24.033$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.b 882.n 7.d $4$ $24.033$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
882.3.n.c 882.n 7.d $4$ $24.033$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+\cdots\)
882.3.n.d 882.n 7.d $4$ $24.033$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.e 882.n 7.d $4$ $24.033$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+\cdots\)
882.3.n.f 882.n 7.d $8$ $24.033$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.g 882.n 7.d $8$ $24.033$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{6})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.h 882.n 7.d $8$ $24.033$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{6})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.i 882.n 7.d $8$ $24.033$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(-2-2\beta _{1})q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
882.3.n.j 882.n 7.d $8$ $24.033$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(-2-2\beta _{4})q^{4}+(-4\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.k 882.n 7.d $8$ $24.033$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(-2-2\beta _{4})q^{4}+(4\beta _{2}+2\beta _{5}+\cdots)q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)