Properties

Label 882.3.b
Level $882$
Weight $3$
Character orbit 882.b
Rep. character $\chi_{882}(197,\cdot)$
Character field $\Q$
Dimension $26$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 368 26 342
Cusp forms 304 26 278
Eisenstein series 64 0 64

Trace form

\( 26q - 52q^{4} + O(q^{10}) \) \( 26q - 52q^{4} - 20q^{10} + 16q^{13} + 104q^{16} - 48q^{19} + 48q^{22} - 74q^{25} - 104q^{31} + 68q^{34} + 36q^{37} + 40q^{40} - 264q^{43} - 176q^{46} - 32q^{52} + 320q^{55} - 76q^{58} - 332q^{61} - 208q^{64} - 520q^{67} + 128q^{73} + 96q^{76} + 576q^{79} + 348q^{82} - 332q^{85} - 96q^{88} - 144q^{94} - 64q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
882.3.b.a \(2\) \(24.033\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
882.3.b.b \(2\) \(24.033\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
882.3.b.c \(2\) \(24.033\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\)
882.3.b.d \(2\) \(24.033\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-2q^{4}+\beta q^{5}+2\beta q^{8}+2q^{10}+\cdots\)
882.3.b.e \(2\) \(24.033\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
882.3.b.f \(4\) \(24.033\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{1}q^{8}+\cdots\)
882.3.b.g \(4\) \(24.033\) \(\Q(\sqrt{-2}, \sqrt{37})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
882.3.b.h \(4\) \(24.033\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
882.3.b.i \(4\) \(24.033\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-2q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)