Space of modular forms of level 3080, weight 2, and trivial character

• Label: 3080.2.a
• Level: $3080$
• Weight: $2$
• Character orbit: 3080.a
• Rep. character: $\chi_{3080}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $21$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3080 = 2^{3} \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3080.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3080))\).

	Total	New	Old
Modular forms	592	60	532
Cusp forms	561	60	501
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.

\(2\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(3\)
Plus space				\(+\)	\(22\)
Minus space				\(-\)	\(38\)

Trace form

\( 60 q + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3080))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	11
3080.2.a.a	$3080$	$2$	3080.a	1.a	$1$	$1$	$1$	$24.594$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{15}+\cdots\)
3080.2.a.b	$3080$	$2$	3080.a	1.a	$1$	$1$	$1$	$24.594$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
3080.2.a.c	$3080$	$2$	3080.a	1.a	$1$	$1$	$1$	$24.594$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots\)
3080.2.a.d	$3080$	$2$	3080.a	1.a	$1$	$1$	$1$	$24.594$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
3080.2.a.e	$3080$	$2$	3080.a	1.a	$1$	$1$	$1$	$24.594$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+q^{11}-6q^{13}+\cdots\)
3080.2.a.f	$3080$	$2$	3080.a	1.a	$1$	$2$	$2$	$24.594$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-q^{11}+\beta q^{13}+\cdots\)
3080.2.a.g	$3080$	$2$	3080.a	1.a	$1$	$2$	$2$	$24.594$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+q^{7}+5q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
3080.2.a.h	$3080$	$2$	3080.a	1.a	$1$	$2$	$2$	$24.594$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-q^{7}-q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
3080.2.a.i	$3080$	$2$	3080.a	1.a	$1$	$2$	$2$	$24.594$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+q^{7}-q^{9}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
3080.2.a.j	$3080$	$2$	3080.a	1.a	$1$	$3$	$3$	$24.594$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+q^{5}+q^{7}+(3\beta _{1}+\beta _{2})q^{9}+\cdots\)
3080.2.a.k	$3080$	$2$	3080.a	1.a	$1$	$3$	$3$	$24.594$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3080.2.a.l	$3080$	$2$	3080.a	1.a	$1$	$3$	$3$	$24.594$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
3080.2.a.m	$3080$	$2$	3080.a	1.a	$1$	$3$	$3$	$24.594$	3.3.404.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}-q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
3080.2.a.n	$3080$	$2$	3080.a	1.a	$1$	$3$	$3$	$24.594$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+q^{7}+(3-\beta _{1}+\beta _{2})q^{9}+\cdots\)
3080.2.a.o	$3080$	$2$	3080.a	1.a	$1$	$4$	$4$	$24.594$	4.4.11348.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}-q^{7}+(-\beta _{2}-\beta _{3})q^{9}+\cdots\)
3080.2.a.p	$3080$	$2$	3080.a	1.a	$1$	$4$	$4$	$24.594$	4.4.116404.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}-q^{7}+(2+\beta _{2})q^{9}-q^{11}+\cdots\)
3080.2.a.q	$3080$	$2$	3080.a	1.a	$1$	$4$	$4$	$24.594$	4.4.25488.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
3080.2.a.r	$3080$	$2$	3080.a	1.a	$1$	$5$	$5$	$24.594$	5.5.549616.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-5\)	\(-5\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}-q^{7}+(1+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
3080.2.a.s	$3080$	$2$	3080.a	1.a	$1$	$5$	$5$	$24.594$	5.5.265504.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-5\)	\(-5\)		$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}-q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
3080.2.a.t	$3080$	$2$	3080.a	1.a	$1$	$5$	$5$	$24.594$	5.5.8892720.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-5\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
3080.2.a.u	$3080$	$2$	3080.a	1.a	$1$	$5$	$5$	$24.594$	5.5.15785648.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(5\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+q^{7}+(3+\beta _{2})q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1540))\)\(^{\oplus 2}\)