Properties

Label 882.3.n
Level $882$
Weight $3$
Character orbit 882.n
Rep. character $\chi_{882}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $11$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
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 736 68 668
Cusp forms 608 68 540
Eisenstein series 128 0 128

Trace form

\( 68q - 68q^{4} + 6q^{5} + O(q^{10}) \) \( 68q - 68q^{4} + 6q^{5} + 24q^{10} + 18q^{11} - 136q^{16} - 78q^{17} - 66q^{19} + 88q^{22} + 82q^{23} + 148q^{25} + 120q^{26} + 160q^{29} - 18q^{31} - 58q^{37} + 12q^{38} - 48q^{40} + 80q^{43} + 36q^{44} + 36q^{46} + 42q^{47} - 304q^{50} + 48q^{52} + 30q^{53} + 64q^{58} - 102q^{59} + 402q^{61} + 544q^{64} - 144q^{65} + 210q^{67} + 156q^{68} + 400q^{71} + 30q^{73} + 264q^{74} - 334q^{79} - 24q^{80} - 264q^{82} + 60q^{85} + 80q^{86} - 88q^{88} - 450q^{89} - 328q^{92} - 372q^{94} - 190q^{95} + O(q^{100}) \)

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.n.a \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-12\) \(0\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.b \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
882.3.n.c \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+\cdots\)
882.3.n.d \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(12\) \(0\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.e \(4\) \(24.033\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(12\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-2-2\beta _{2})q^{4}+\cdots\)
882.3.n.f \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
882.3.n.g \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{6})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.h \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{6})q^{2}+2\beta _{4}q^{4}+(\beta _{1}+2\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.i \(8\) \(24.033\) 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(-2-2\beta _{1})q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
882.3.n.j \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-2-2\beta _{4})q^{4}+(-4\beta _{3}+\cdots)q^{5}+\cdots\)
882.3.n.k \(8\) \(24.033\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-2-2\beta _{4})q^{4}+(4\beta _{2}+2\beta _{5}+\cdots)q^{5}+\cdots\)

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

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