Space of modular forms of level 2940, weight 2, and trivial character

• Label: 2940.2.a
• Level: $2940$
• Weight: $2$
• Character orbit: 2940.a
• Rep. character: $\chi_{2940}(1,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• 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.a (trivial)
Character field:			\(\Q\)
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 \(M_{2}(\Gamma_0(2940))\).

	Total	New	Old
Modular forms	720	28	692
Cusp forms	625	28	597
Eisenstein series	95	0	95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	\(7\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(40\)	\(0\)	\(40\)		\(33\)	\(0\)	\(33\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(51\)	\(0\)	\(51\)		\(43\)	\(0\)	\(43\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(52\)	\(0\)	\(52\)		\(44\)	\(0\)	\(44\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(41\)	\(0\)	\(41\)		\(33\)	\(0\)	\(33\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(48\)	\(0\)	\(48\)		\(40\)	\(0\)	\(40\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(43\)	\(0\)	\(43\)		\(35\)	\(0\)	\(35\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(44\)	\(0\)	\(44\)		\(36\)	\(0\)	\(36\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(49\)	\(0\)	\(49\)		\(41\)	\(0\)	\(41\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(44\)	\(3\)	\(41\)		\(40\)	\(3\)	\(37\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(45\)	\(4\)	\(41\)		\(41\)	\(4\)	\(37\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(44\)	\(3\)	\(41\)		\(40\)	\(3\)	\(37\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(43\)	\(4\)	\(39\)		\(39\)	\(4\)	\(35\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(48\)	\(4\)	\(44\)		\(44\)	\(4\)	\(40\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(41\)	\(3\)	\(38\)		\(37\)	\(3\)	\(34\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(40\)	\(4\)	\(36\)		\(36\)	\(4\)	\(32\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(47\)	\(3\)	\(44\)		\(43\)	\(3\)	\(40\)		\(4\)	\(0\)	\(4\)
Plus space				\(+\)		\(352\)	\(14\)	\(338\)		\(305\)	\(14\)	\(291\)		\(47\)	\(0\)	\(47\)
Minus space				\(-\)		\(368\)	\(14\)	\(354\)		\(320\)	\(14\)	\(306\)		\(48\)	\(0\)	\(48\)

Trace form

28 * q + 28 * q^9 - 8 * q^11 - 8 * q^13 - 16 * q^17 - 8 * q^19 + 28 * q^25 - 8 * q^29 + 8 * q^31 - 8 * q^33 - 36 * q^37 - 20 * q^39 - 36 * q^43 + 16 * q^47 - 8 * q^51 + 8 * q^55 - 20 * q^57 + 16 * q^59 - 8 * q^61 - 8 * q^65 - 20 * q^67 - 8 * q^69 + 16 * q^71 + 8 * q^73 - 4 * q^79 + 28 * q^81 + 16 * q^83 + 8 * q^85 + 16 * q^89 - 4 * q^93 + 8 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\) 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					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	7
2940.2.a.a	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓	✓			2940.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-6q^{11}+q^{15}+6q^{17}+\cdots\)
2940.2.a.b	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.q.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+7q^{13}+\cdots\)
2940.2.a.c	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.d	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}-q^{15}+\cdots\)
2940.2.a.e	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓	✓			2940.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.f	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2940.2.a.g	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2940.2.a.h	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.q.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{11}-q^{13}-q^{15}+\cdots\)
2940.2.a.i	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓	✓			2940.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
2940.2.a.j	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓	✓			2940.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-6q^{11}+q^{15}-6q^{17}+\cdots\)
2940.2.a.k	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.q.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}-7q^{13}+\cdots\)
2940.2.a.l	$2940$	$2$	2940.a	1.a	$1$	$1$	$1$	$23.476$	\(\Q\)	None	✓				420.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2940.2.a.m	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{7}) \)	None	✓		✓		420.2.q.c	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+(1+\beta )q^{11}-\beta q^{13}+\cdots\)
2940.2.a.n	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		2940.2.a.n	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+(2+2\beta )q^{11}+q^{15}+\cdots\)
2940.2.a.o	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		2940.2.a.o	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
2940.2.a.p	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓		✓		420.2.q.d	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+\beta q^{11}+(1+\beta )q^{13}+\cdots\)
2940.2.a.q	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓	✓			2940.2.a.o	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
2940.2.a.r	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓				420.2.q.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+\beta q^{11}+(-1-\beta )q^{13}+\cdots\)
2940.2.a.s	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{7}) \)	None	✓				420.2.q.c	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+(1+\beta )q^{11}+\beta q^{13}+\cdots\)
2940.2.a.t	$2940$	$2$	2940.a	1.a	$1$	$2$	$2$	$23.476$	\(\Q(\sqrt{2}) \)	None	✓	✓			2940.2.a.n	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+(2+2\beta )q^{11}+q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2940))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2940)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 2}\)