Space of modular forms of level 882, weight 2, and Character 882.k

• Label: 882.2.k
• Level: $882$
• Weight: $2$
• Character orbit: 882.k
• Rep. character: $\chi_{882}(215,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

	Total	New	Old
Modular forms	400	24	376
Cusp forms	272	24	248
Eisenstein series	128	0	128

Trace form

24 * q + 12 * q^4 - 12 * q^10 - 12 * q^16 + 24 * q^19 + 40 * q^22 + 8 * q^25 + 12 * q^31 - 48 * q^37 - 12 * q^40 + 96 * q^43 - 20 * q^58 - 24 * q^61 - 24 * q^64 + 8 * q^67 - 24 * q^73 + 28 * q^79 - 48 * q^82 + 20 * q^88 + 24 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.2.k.a	$882$	$2$	882.k	21.g	$6$	$8$	$4$	$7.043$	\(\Q(\zeta_{24})\)	None					126.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_1 q^{2}+\beta_{2} q^{4}+(-\beta_{6}+\beta_{5}+\cdots+\beta_1)q^{5}+\cdots\)
882.2.k.b	$882$	$2$	882.k	21.g	$6$	$16$	$8$	$7.043$	\(\Q(\zeta_{48})\)	None		✓	✓		882.2.d.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{5}-\beta_1)q^{2}+(-\beta_{3}+1)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

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