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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
882.2.g.a \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
882.2.g.b \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
882.2.g.c \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}-4q^{13}+\cdots\)
882.2.g.d \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+q^{8}+4q^{13}+\cdots\)
882.2.g.e \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
882.2.g.f \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
882.2.g.g \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
882.2.g.h \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
882.2.g.i \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}-q^{8}+\cdots\)
882.2.g.j \(2\) \(7.043\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
882.2.g.k \(4\) \(7.043\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+q^{8}+\cdots\)
882.2.g.l \(4\) \(7.043\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}-q^{8}+\cdots\)
882.2.g.m \(4\) \(7.043\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}-q^{8}+\cdots\)

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

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