Space of modular forms of level 4624, weight 2, and trivial character

• Label: 4624.2.a
• Level: $4624$
• Weight: $2$
• Character orbit: 4624.a
• Rep. character: $\chi_{4624}(1,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $46$
• Sturm bound: $1224$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 4624 = 2^{4} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4624.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1224\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4624))\).

	Total	New	Old
Modular forms	666	143	523
Cusp forms	559	128	431
Eisenstein series	107	15	92

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

\(2\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(32\)
\(+\)	\(-\)	$-$	\(36\)
\(-\)	\(+\)	$-$	\(32\)
\(-\)	\(-\)	$+$	\(28\)
Plus space		\(+\)	\(60\)
Minus space		\(-\)	\(68\)

Trace form

\( 128 q - 2 q^{3} - 2 q^{7} + 112 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4624))\) 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	17
4624.2.a.a	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4624.2.a.b	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
4624.2.a.c	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
4624.2.a.d	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-3q^{9}-2q^{13}+4q^{19}+\cdots\)
4624.2.a.e	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
4624.2.a.f	$4624$	$2$	4624.a	1.a	$1$	$1$	$1$	$36.923$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+2q^{11}-6q^{13}-4q^{19}+\cdots\)
4624.2.a.g	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-\beta q^{5}+\beta q^{7}+(1+3\beta )q^{9}+\cdots\)
4624.2.a.h	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-2q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
4624.2.a.i	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+3\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
4624.2.a.j	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
4624.2.a.k	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}+(-3+\beta )q^{7}+(2+\cdots)q^{9}+\cdots\)
4624.2.a.l	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-3q^{9}-4\beta q^{11}-4q^{13}+4q^{19}+\cdots\)
4624.2.a.m	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{7}-3q^{9}-2\beta q^{11}+2q^{13}+\cdots\)
4624.2.a.n	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
4624.2.a.o	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+2\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
4624.2.a.p	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}+\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
4624.2.a.q	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+3\beta q^{5}-3\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
4624.2.a.r	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}-2\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
4624.2.a.s	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}+5q^{9}+\beta q^{11}+2q^{13}+\cdots\)
4624.2.a.t	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}-\beta q^{5}-2\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
4624.2.a.u	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+(2+\cdots)q^{9}+\cdots\)
4624.2.a.v	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+(1+\beta )q^{7}+\beta q^{9}+\cdots\)
4624.2.a.w	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-3\beta )q^{5}+(3-\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
4624.2.a.x	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+2\beta q^{5}+(-1-\beta )q^{7}+\cdots\)
4624.2.a.y	$4624$	$2$	4624.a	1.a	$1$	$2$	$2$	$36.923$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+\beta q^{5}-\beta q^{7}+(1+3\beta )q^{9}+\cdots\)
4624.2.a.z	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4624.2.a.ba	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
4624.2.a.bb	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(6\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1})q^{5}+\cdots\)
4624.2.a.bc	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(6\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4624.2.a.bd	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4624.2.a.be	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(6\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4624.2.a.bf	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4624.2.a.bg	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4624.2.a.bh	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4624.2.a.bi	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-6\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-2-\beta _{1})q^{5}+\cdots\)
4624.2.a.bj	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+2\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-2\beta _{2})q^{5}+\cdots\)
4624.2.a.bk	$4624$	$2$	4624.a	1.a	$1$	$3$	$3$	$36.923$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(6\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
4624.2.a.bl	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
4624.2.a.bm	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2\beta _{1}-\beta _{3})q^{7}+\cdots\)
4624.2.a.bn	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-2\beta _{1}q^{5}-2\beta _{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)
4624.2.a.bo	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}+(2\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4624.2.a.bp	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
4624.2.a.bq	$4624$	$2$	4624.a	1.a	$1$	$4$	$4$	$36.923$	\(\Q(\sqrt{2}, \sqrt{13})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4624.2.a.br	$4624$	$2$	4624.a	1.a	$1$	$6$	$6$	$36.923$	6.6.3418281.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
4624.2.a.bs	$4624$	$2$	4624.a	1.a	$1$	$6$	$6$	$36.923$	6.6.3418281.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(6\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
4624.2.a.bt	$4624$	$2$	4624.a	1.a	$1$	$12$	$12$	$36.923$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{6}q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2312))\)\(^{\oplus 2}\)