Space of modular forms of level 3040, weight 2, and trivial character

• Label: 3040.2.a
• Level: $3040$
• Weight: $2$
• Character orbit: 3040.a
• Rep. character: $\chi_{3040}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $24$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3040.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3040))\).

	Total	New	Old
Modular forms	496	72	424
Cusp forms	465	72	393
Eisenstein series	31	0	31

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

\(2\)	\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(56\)	\(10\)	\(46\)		\(53\)	\(10\)	\(43\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(66\)	\(8\)	\(58\)		\(62\)	\(8\)	\(54\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(68\)	\(11\)	\(57\)		\(64\)	\(11\)	\(53\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(58\)	\(7\)	\(51\)		\(54\)	\(7\)	\(47\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(60\)	\(8\)	\(52\)		\(56\)	\(8\)	\(48\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(66\)	\(10\)	\(56\)		\(62\)	\(10\)	\(52\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(64\)	\(7\)	\(57\)		\(60\)	\(7\)	\(53\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(58\)	\(11\)	\(47\)		\(54\)	\(11\)	\(43\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(244\)	\(34\)	\(210\)		\(229\)	\(34\)	\(195\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(252\)	\(38\)	\(214\)		\(236\)	\(38\)	\(198\)		\(16\)	\(0\)	\(16\)

Trace form

\( 72 q + 72 q^{9} - 16 q^{21} + 72 q^{25} - 16 q^{29} - 16 q^{45} + 72 q^{49} - 80 q^{69} - 64 q^{77} + 120 q^{81} + 48 q^{89} - 64 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3040))\) 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	5	19
3040.2.a.a	$3040$	$2$	3040.a	1.a	$1$	$1$	$1$	$24.275$	\(\Q\)	None	✓	✓			3040.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}-2q^{9}+5q^{13}+\cdots\)
3040.2.a.b	$3040$	$2$	3040.a	1.a	$1$	$1$	$1$	$24.275$	\(\Q\)	None	✓	✓			3040.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots\)
3040.2.a.c	$3040$	$2$	3040.a	1.a	$1$	$1$	$1$	$24.275$	\(\Q\)	None	✓	✓			3040.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\)
3040.2.a.d	$3040$	$2$	3040.a	1.a	$1$	$1$	$1$	$24.275$	\(\Q\)	None	✓	✓			3040.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}-2q^{9}+5q^{13}+\cdots\)
3040.2.a.e	$3040$	$2$	3040.a	1.a	$1$	$2$	$2$	$24.275$	\(\Q(\sqrt{17}) \)	None	✓	✓			3040.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3040.2.a.f	$3040$	$2$	3040.a	1.a	$1$	$2$	$2$	$24.275$	\(\Q(\sqrt{2}) \)	None	✓	✓			3040.2.a.f	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}-3q^{9}-4q^{11}+(2+\beta )q^{13}+\cdots\)
3040.2.a.g	$3040$	$2$	3040.a	1.a	$1$	$2$	$2$	$24.275$	\(\Q(\sqrt{2}) \)	None	✓	✓			3040.2.a.f	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}-3q^{9}+4q^{11}+(2+\beta )q^{13}+\cdots\)
3040.2.a.h	$3040$	$2$	3040.a	1.a	$1$	$2$	$2$	$24.275$	\(\Q(\sqrt{17}) \)	None	✓	✓			3040.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3040.2.a.i	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.i	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3040.2.a.j	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.j	$1$	$1$	\(0\)	\(-4\)	\(3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3040.2.a.k	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.564.1	None	✓	✓			3040.2.a.k	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
3040.2.a.l	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.l	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
3040.2.a.m	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.l	$1$	$1$	\(0\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
3040.2.a.n	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.564.1	None	✓	✓			3040.2.a.k	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
3040.2.a.o	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.i	$1$	$0$	\(0\)	\(4\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
3040.2.a.p	$3040$	$2$	3040.a	1.a	$1$	$3$	$3$	$24.275$	3.3.148.1	None	✓	✓			3040.2.a.j	$1$	$0$	\(0\)	\(4\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
3040.2.a.q	$3040$	$2$	3040.a	1.a	$1$	$4$	$4$	$24.275$	4.4.78292.1	None	✓	✓	✓		3040.2.a.q	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3040.2.a.r	$3040$	$2$	3040.a	1.a	$1$	$4$	$4$	$24.275$	4.4.17428.1	None	✓	✓	✓		3040.2.a.r	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
3040.2.a.s	$3040$	$2$	3040.a	1.a	$1$	$4$	$4$	$24.275$	4.4.78292.1	None	✓	✓			3040.2.a.q	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3040.2.a.t	$3040$	$2$	3040.a	1.a	$1$	$4$	$4$	$24.275$	4.4.17428.1	None	✓	✓			3040.2.a.r	$1$	$0$	\(0\)	\(1\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
3040.2.a.u	$3040$	$2$	3040.a	1.a	$1$	$5$	$5$	$24.275$	5.5.387268.1	None	✓	✓	✓		3040.2.a.u	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-q^{5}+(1+\beta _{4})q^{7}+\cdots\)
3040.2.a.v	$3040$	$2$	3040.a	1.a	$1$	$5$	$5$	$24.275$	5.5.2363492.1	None	✓	✓	✓		3040.2.a.v	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
3040.2.a.w	$3040$	$2$	3040.a	1.a	$1$	$5$	$5$	$24.275$	5.5.2363492.1	None	✓	✓	✓		3040.2.a.v	$1$	$0$	\(0\)	\(2\)	\(5\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}-\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
3040.2.a.x	$3040$	$2$	3040.a	1.a	$1$	$5$	$5$	$24.275$	5.5.387268.1	None	✓	✓	✓		3040.2.a.u	$1$	$1$	\(0\)	\(4\)	\(-5\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-q^{5}+(-1-\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3040)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)