Properties

Label 882.3.c
Level $882$
Weight $3$
Character orbit 882.c
Rep. character $\chi_{882}(685,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $7$
Sturm bound $504$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(504\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(882, [\chi])\).

Total New Old
Modular forms 368 32 336
Cusp forms 304 32 272
Eisenstein series 64 0 64

Trace form

\( 32 q + 64 q^{4} + O(q^{10}) \) \( 32 q + 64 q^{4} - 36 q^{11} + 128 q^{16} - 40 q^{22} - 4 q^{23} - 36 q^{25} + 176 q^{29} + 20 q^{37} + 32 q^{43} - 72 q^{44} - 72 q^{46} + 88 q^{50} - 204 q^{53} + 104 q^{58} + 256 q^{64} + 480 q^{65} - 292 q^{67} - 64 q^{71} + 72 q^{74} - 228 q^{79} - 132 q^{85} - 320 q^{86} - 80 q^{88} - 8 q^{92} - 212 q^{95} + O(q^{100}) \)

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.c.a \(4\) \(24.033\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+4\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\)
882.3.c.b \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-2\beta _{3})q^{5}-2\beta _{1}q^{8}+\cdots\)
882.3.c.c \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2q^{4}+2\beta _{3}q^{5}-2\beta _{1}q^{8}+\cdots\)
882.3.c.d \(4\) \(24.033\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\)
882.3.c.e \(4\) \(24.033\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots\)
882.3.c.f \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+2q^{4}+(\beta _{2}+2\beta _{3})q^{5}+2\beta _{1}q^{8}+\cdots\)
882.3.c.g \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+2q^{4}+(-\beta _{2}-\beta _{4})q^{5}+2\beta _{1}q^{8}+\cdots\)

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

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