Space of modular forms of level 3042, weight 3, and Character 3042.d

• Label: 3042.3.d
• Level: $3042$
• Weight: $3$
• Character orbit: 3042.d
• Rep. character: $\chi_{3042}(3041,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $8$
• Sturm bound: $1638$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3042.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1638\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3042, [\chi])\).

	Total	New	Old
Modular forms	1148	100	1048
Cusp forms	1036	100	936
Eisenstein series	112	0	112

Trace form

\( 100 q + 200 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3042, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3042.3.d.a	$3042$	$3$	3042.d	39.d	$2$	$4$	$4$	$82.888$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+2q^{4}-3\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{7}+\cdots\)
3042.3.d.b	$3042$	$3$	3042.d	39.d	$2$	$4$	$4$	$82.888$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{3}q^{5}+5\zeta_{8}q^{7}+\cdots\)
3042.3.d.c	$3042$	$3$	3042.d	39.d	$2$	$8$	$8$	$82.888$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+2q^{4}+(-\beta _{3}-\beta _{6})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
3042.3.d.d	$3042$	$3$	3042.d	39.d	$2$	$8$	$8$	$82.888$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+2q^{4}+(3\beta _{3}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3042.3.d.e	$3042$	$3$	3042.d	39.d	$2$	$12$	$12$	$82.888$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+2q^{4}+\beta _{7}q^{5}+(2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
3042.3.d.f	$3042$	$3$	3042.d	39.d	$2$	$16$	$16$	$82.888$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+2q^{4}+(-\beta _{10}-\beta _{11})q^{5}+\cdots\)
3042.3.d.g	$3042$	$3$	3042.d	39.d	$2$	$24$	$24$	$82.888$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
3042.3.d.h	$3042$	$3$	3042.d	39.d	$2$	$24$	$24$	$82.888$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(3042, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3042, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1521, [\chi])\)\(^{\oplus 2}\)