Space of modular forms of level 6084, weight 2, and Character 6084.b

• Label: 6084.2.b
• Level: $6084$
• Weight: $2$
• Character orbit: 6084.b
• Rep. character: $\chi_{6084}(4393,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $19$
• Sturm bound: $2184$
• Trace bound: $43$

Defining parameters

Level:	\( N \)	\(=\)	\( 6084 = 2^{2} \cdot 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6084.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(2184\)
Trace bound:			\(43\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6084, [\chi])\).

	Total	New	Old
Modular forms	1176	64	1112
Cusp forms	1008	64	944
Eisenstein series	168	0	168

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6084, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
6084.2.b.a	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{7}-6q^{17}+iq^{19}+5q^{25}+6q^{29}+\cdots\)
6084.2.b.b	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+iq^{7}-2iq^{11}-4q^{17}+\cdots\)
6084.2.b.c	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{5}+2\zeta_{6}q^{7}+2\zeta_{6}q^{11}-3q^{17}+\cdots\)
6084.2.b.d	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-3q^{17}+3\zeta_{6}q^{19}+\cdots\)
6084.2.b.e	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+2iq^{7}+2iq^{11}-8q^{23}+\cdots\)
6084.2.b.f	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2iq^{7}-4iq^{19}+5q^{25}+2iq^{31}+\cdots\)
6084.2.b.g	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+5iq^{7}-8iq^{19}+5q^{25}-11iq^{31}+\cdots\)
6084.2.b.h	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{7}+2\zeta_{6}q^{19}+5q^{25}-\zeta_{6}q^{31}+\cdots\)
6084.2.b.i	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-2iq^{7}+2iq^{11}+8q^{23}+\cdots\)
6084.2.b.j	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+iq^{7}-2iq^{11}+2q^{17}+\cdots\)
6084.2.b.k	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}+4iq^{7}+3q^{17}+2iq^{19}+\cdots\)
6084.2.b.l	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+iq^{7}+5iq^{11}+3q^{17}+\cdots\)
6084.2.b.m	$6084$	$2$	6084.b	13.b	$2$	$2$	$2$	$48.581$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-iq^{7}+iq^{11}+6q^{17}+3iq^{19}+\cdots\)
6084.2.b.n	$6084$	$2$	6084.b	13.b	$2$	$4$	$4$	$48.581$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-2\beta _{1}q^{7}+2\beta _{3}q^{11}-3\beta _{2}q^{17}+\cdots\)
6084.2.b.o	$6084$	$2$	6084.b	13.b	$2$	$4$	$4$	$48.581$	\(\Q(\sqrt{-3}, \sqrt{-43})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{11}+\cdots\)
6084.2.b.p	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-3\beta _{5})q^{5}+(-3\beta _{1}+2\beta _{3}+2\beta _{5})q^{7}+\cdots\)
6084.2.b.q	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3}+2\beta _{5})q^{7}+\cdots\)
6084.2.b.r	$6084$	$2$	6084.b	13.b	$2$	$6$	$6$	$48.581$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}-\beta _{3}-3\beta _{5})q^{7}+\cdots\)
6084.2.b.s	$6084$	$2$	6084.b	13.b	$2$	$12$	$12$	$48.581$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{4}-\beta _{9}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6084, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6084, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 3}\)