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Properties

Label 882.2.g
Level $882$
Weight $2$
Character orbit 882.g
Rep. character $\chi_{882}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $13$
Sturm bound $336$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(336\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

Total New Old
Modular forms 400 32 368
Cusp forms 272 32 240
Eisenstein series 128 0 128

Trace form

\( 32 q - 16 q^{4} - 4 q^{5} + O(q^{10}) \) \( 32 q - 16 q^{4} - 4 q^{5} + 4 q^{10} - 12 q^{11} - 16 q^{16} + 4 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 4 q^{23} - 12 q^{25} - 4 q^{26} + 8 q^{29} - 12 q^{31} - 16 q^{34} + 8 q^{37} - 12 q^{38} + 4 q^{40} - 24 q^{43} - 12 q^{44} - 24 q^{46} + 12 q^{47} + 32 q^{50} - 12 q^{53} + 8 q^{55} - 20 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 32 q^{64} - 4 q^{65} + 24 q^{67} + 4 q^{68} - 8 q^{71} + 16 q^{73} - 4 q^{74} - 16 q^{76} + 60 q^{79} - 4 q^{80} - 32 q^{83} - 48 q^{85} - 16 q^{86} - 8 q^{88} - 8 q^{92} + 24 q^{94} + 4 q^{95} + 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.2.g.a 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 294.2.a.b \(-1\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
882.2.g.b 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 42.2.e.b \(-1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
882.2.g.c 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 14.2.a.a \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}-4q^{13}+\cdots\)
882.2.g.d 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 14.2.a.a \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}+4q^{13}+\cdots\)
882.2.g.e 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 126.2.g.a \(-1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
882.2.g.f 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 294.2.a.b \(-1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
882.2.g.g 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 126.2.g.a \(1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
882.2.g.h 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 42.2.a.a \(1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
882.2.g.i 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 42.2.e.a \(1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}-q^{8}+\cdots\)
882.2.g.j 882.g 7.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None 42.2.a.a \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
882.2.g.k 882.g 7.c $4$ $7.043$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 882.2.a.m \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+q^{8}+\cdots\)
882.2.g.l 882.g 7.c $4$ $7.043$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 98.2.a.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}-q^{8}+\cdots\)
882.2.g.m 882.g 7.c $4$ $7.043$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 882.2.a.m \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}-q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

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