Space of modular forms of level 2940, weight 2, and Character 2940.q

• Label: 2940.2.q
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.q
• Rep. character: $\chi_{2940}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $52$
• Newform subspaces: $20$
• Sturm bound: $1344$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1344\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

	Total	New	Old
Modular forms	1440	52	1388
Cusp forms	1248	52	1196
Eisenstein series	192	0	192

Trace form

\( 52 q + 2 q^{3} - 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2940.2.q.a	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.b	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.d	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.c	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.q.b	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2940.2.q.d	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None		✓			2940.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(6+\cdots)q^{11}+\cdots\)
2940.2.q.e	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.c	$2$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2940.2.q.f	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None		✓			2940.2.a.e	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.g	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2940.2.q.h	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.q.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2940.2.q.i	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.c	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2940.2.q.j	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None		✓			2940.2.a.e	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.k	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.b	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2940.2.q.l	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.d	$2$	$1$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.m	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None					420.2.a.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.n	$2940$	$2$	2940.q	7.c	$3$	$2$	$1$	$23.476$	\(\Q(\sqrt{-3}) \)	None		✓			2940.2.a.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
2940.2.q.o	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			2940.2.a.n	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.p	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			2940.2.a.o	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{2})q^{9}+\cdots\)
2940.2.q.q	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					420.2.q.d	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{9}+\beta _{1}q^{11}+\cdots\)
2940.2.q.r	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			2940.2.a.o	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
2940.2.q.s	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			2940.2.a.n	$2$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}-\beta _{2}q^{5}+\beta _{2}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2940.2.q.t	$2940$	$2$	2940.q	7.c	$3$	$4$	$2$	$23.476$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None					420.2.q.c	$2$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}-\beta _{2}q^{5}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)