Properties

Label 882.5.b
Level $882$
Weight $5$
Character orbit 882.b
Rep. character $\chi_{882}(197,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $10$
Sturm bound $840$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 882.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(840\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(882, [\chi])\).

Total New Old
Modular forms 704 56 648
Cusp forms 640 56 584
Eisenstein series 64 0 64

Trace form

\( 56q - 448q^{4} + O(q^{10}) \) \( 56q - 448q^{4} + 128q^{10} - 560q^{13} + 3584q^{16} + 1040q^{19} - 7560q^{25} + 880q^{31} - 2048q^{34} + 392q^{37} - 1024q^{40} + 6776q^{43} + 3584q^{46} + 4480q^{52} + 1168q^{55} - 896q^{58} + 8032q^{61} - 28672q^{64} - 4200q^{67} + 27360q^{73} - 8320q^{76} + 13496q^{79} - 18432q^{82} - 46144q^{85} + 39168q^{94} - 7872q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
882.5.b.a \(4\) \(91.172\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}-8q^{4}+(5\beta _{1}+\beta _{2})q^{5}-2^{4}\beta _{1}q^{8}+\cdots\)
882.5.b.b \(4\) \(91.172\) \(\Q(\sqrt{-2}, \sqrt{-29})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}-8q^{4}+\beta _{3}q^{5}-2^{4}\beta _{1}q^{8}+\cdots\)
882.5.b.c \(4\) \(91.172\) \(\Q(\sqrt{-2}, \sqrt{-53})\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{3}q^{5}+2^{4}\beta _{1}q^{8}+\cdots\)
882.5.b.d \(4\) \(91.172\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}-8q^{4}+(-13\beta _{1}+\beta _{2})q^{5}+\cdots\)
882.5.b.e \(6\) \(91.172\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}-8q^{4}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
882.5.b.f \(6\) \(91.172\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}-8q^{4}+(2\beta _{1}-\beta _{2})q^{5}-2^{4}\beta _{1}q^{8}+\cdots\)
882.5.b.g \(6\) \(91.172\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}-8q^{4}+(2\beta _{1}-\beta _{2})q^{5}+2^{4}\beta _{1}q^{8}+\cdots\)
882.5.b.h \(6\) \(91.172\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}-8q^{4}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
882.5.b.i \(8\) \(91.172\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}-8q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
882.5.b.j \(8\) \(91.172\) 8.0.\(\cdots\).12 None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{2}q^{2}-8q^{4}-\beta _{3}q^{5}+2^{4}\beta _{2}q^{8}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)