Properties

Label 882.5.c
Level $882$
Weight $5$
Character orbit 882.c
Rep. character $\chi_{882}(685,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $10$
Sturm bound $840$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 882.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(840\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 704 68 636
Cusp forms 640 68 572
Eisenstein series 64 0 64

Trace form

\( 68q + 544q^{4} + O(q^{10}) \) \( 68q + 544q^{4} + 108q^{11} + 4352q^{16} - 1088q^{22} - 972q^{23} - 10088q^{25} - 456q^{29} + 6644q^{37} - 3616q^{43} + 864q^{44} - 7680q^{46} - 14976q^{50} + 9588q^{53} - 2048q^{58} + 34816q^{64} + 72q^{65} + 5124q^{67} - 45744q^{71} + 14016q^{74} + 8420q^{79} + 35004q^{85} + 12672q^{86} - 8704q^{88} - 7776q^{92} + 79668q^{95} + O(q^{100}) \)

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.c.a \(4\) \(91.172\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+8q^{4}+(-11\beta _{2}-\beta _{3})q^{5}+\cdots\)
882.5.c.b \(4\) \(91.172\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+8q^{4}+(-9\beta _{2}-2\beta _{3})q^{5}+\cdots\)
882.5.c.c \(4\) \(91.172\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+8q^{4}+(-5\beta _{1}-13\beta _{3})q^{5}+\cdots\)
882.5.c.d \(4\) \(91.172\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+8q^{4}+(19\beta _{1}+13\beta _{3})q^{5}+\cdots\)
882.5.c.e \(8\) \(91.172\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+8q^{4}+(-3\beta _{1}-2\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
882.5.c.f \(8\) \(91.172\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+8q^{4}+(5\beta _{2}-11\beta _{3})q^{5}+\cdots\)
882.5.c.g \(8\) \(91.172\) 8.0.\(\cdots\).21 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+8q^{4}+(-\beta _{3}-4\beta _{4})q^{5}+\cdots\)
882.5.c.h \(8\) \(91.172\) 8.0.\(\cdots\).21 None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}+8q^{4}+(-\beta _{3}-4\beta _{4})q^{5}+\cdots\)
882.5.c.i \(8\) \(91.172\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+8q^{4}+(-5\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
882.5.c.j \(12\) \(91.172\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+8q^{4}-\beta _{3}q^{5}-8\beta _{1}q^{8}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)