Space of modular forms of level 7248, weight 2, and trivial character

• Label: 7248.2.a
• Level: $7248$
• Weight: $2$
• Character orbit: 7248.a
• Rep. character: $\chi_{7248}(1,\cdot)$
• Character field: $\Q$
• Dimension: $150$
• Newform subspaces: $42$
• Sturm bound: $2432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7248 = 2^{4} \cdot 3 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7248.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(2432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7248))\).

	Total	New	Old
Modular forms	1228	150	1078
Cusp forms	1205	150	1055
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(151\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(+\)	\(-\)	$-$	\(20\)
\(+\)	\(-\)	\(+\)	$-$	\(20\)
\(+\)	\(-\)	\(-\)	$+$	\(17\)
\(-\)	\(+\)	\(+\)	$-$	\(17\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(14\)
\(-\)	\(-\)	\(-\)	$-$	\(24\)
Plus space			\(+\)	\(69\)
Minus space			\(-\)	\(81\)

Trace form

\( 150 q + 4 q^{5} + 150 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7248))\) 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	3	151
7248.2.a.a	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
7248.2.a.b	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots\)
7248.2.a.c	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
7248.2.a.d	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}+5q^{11}-4q^{13}+\cdots\)
7248.2.a.e	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
7248.2.a.f	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots\)
7248.2.a.g	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+6q^{11}-6q^{13}+\cdots\)
7248.2.a.h	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
7248.2.a.i	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
7248.2.a.j	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+3q^{11}+3q^{13}+\cdots\)
7248.2.a.k	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
7248.2.a.l	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{9}+5q^{11}-5q^{13}+\cdots\)
7248.2.a.m	$7248$	$2$	7248.a	1.a	$1$	$1$	$1$	$57.876$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
7248.2.a.n	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}+(-1-2\beta )q^{7}+\cdots\)
7248.2.a.o	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+3q^{7}+q^{9}+(4-2\beta )q^{11}+\cdots\)
7248.2.a.p	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(1+2\beta )q^{7}+q^{9}+\cdots\)
7248.2.a.q	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7248.2.a.r	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
7248.2.a.s	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(-1+2\beta )q^{7}+q^{9}+\cdots\)
7248.2.a.t	$7248$	$2$	7248.a	1.a	$1$	$2$	$2$	$57.876$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
7248.2.a.u	$7248$	$2$	7248.a	1.a	$1$	$3$	$3$	$57.876$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{2})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
7248.2.a.v	$7248$	$2$	7248.a	1.a	$1$	$3$	$3$	$57.876$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+2\beta _{2}q^{7}+\cdots\)
7248.2.a.w	$7248$	$2$	7248.a	1.a	$1$	$3$	$3$	$57.876$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
7248.2.a.x	$7248$	$2$	7248.a	1.a	$1$	$3$	$3$	$57.876$	3.3.621.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(2+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7248.2.a.y	$7248$	$2$	7248.a	1.a	$1$	$3$	$3$	$57.876$	3.3.733.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)
7248.2.a.z	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.58217.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+2q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
7248.2.a.ba	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.2777.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7248.2.a.bb	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.25961.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
7248.2.a.bc	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.2777.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}-2\beta _{1}q^{7}+q^{9}+\cdots\)
7248.2.a.bd	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.16609.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-1\)	\(-7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7248.2.a.be	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.48657.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{3}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
7248.2.a.bf	$7248$	$2$	7248.a	1.a	$1$	$4$	$4$	$57.876$	4.4.16609.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{2}-\beta _{3})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
7248.2.a.bg	$7248$	$2$	7248.a	1.a	$1$	$5$	$5$	$57.876$	5.5.138917.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-4\)	\(8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{3})q^{5}+(2+\beta _{4})q^{7}+\cdots\)
7248.2.a.bh	$7248$	$2$	7248.a	1.a	$1$	$5$	$5$	$57.876$	5.5.459533.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
7248.2.a.bi	$7248$	$2$	7248.a	1.a	$1$	$5$	$5$	$57.876$	5.5.1190005.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(-4\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7248.2.a.bj	$7248$	$2$	7248.a	1.a	$1$	$5$	$5$	$57.876$	5.5.352076.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
7248.2.a.bk	$7248$	$2$	7248.a	1.a	$1$	$8$	$8$	$57.876$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8\)	\(4\)	\(-8\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{4})q^{7}+\cdots\)
7248.2.a.bl	$7248$	$2$	7248.a	1.a	$1$	$9$	$9$	$57.876$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(-2\)	\(-14\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{2}-\beta _{6})q^{5}+(-2+\beta _{4}+\cdots)q^{7}+\cdots\)
7248.2.a.bm	$7248$	$2$	7248.a	1.a	$1$	$10$	$10$	$57.876$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-10\)	\(2\)	\(-8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
7248.2.a.bn	$7248$	$2$	7248.a	1.a	$1$	$10$	$10$	$57.876$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(10\)	\(0\)	\(-12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}-\beta _{4})q^{7}+\cdots\)
7248.2.a.bo	$7248$	$2$	7248.a	1.a	$1$	$11$	$11$	$57.876$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(11\)	\(5\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1-\beta _{5})q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)
7248.2.a.bp	$7248$	$2$	7248.a	1.a	$1$	$12$	$12$	$57.876$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-12\)	\(8\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+\beta _{10}q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(302))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(453))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(604))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(906))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1812))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3624))\)\(^{\oplus 2}\)