Space of modular forms of level 8024, weight 2, and trivial character

• Label: 8024.2.a
• Level: $8024$
• Weight: $2$
• Character orbit: 8024.a
• Rep. character: $\chi_{8024}(1,\cdot)$
• Character field: $\Q$
• Dimension: $232$
• Newform subspaces: $29$
• Sturm bound: $2160$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8024.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(2160\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8024))\).

	Total	New	Old
Modular forms	1088	232	856
Cusp forms	1073	232	841
Eisenstein series	15	0	15

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

\(2\)	\(17\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(28\)
\(+\)	\(+\)	\(-\)	$-$	\(31\)
\(+\)	\(-\)	\(+\)	$-$	\(30\)
\(+\)	\(-\)	\(-\)	$+$	\(27\)
\(-\)	\(+\)	\(+\)	$-$	\(34\)
\(-\)	\(+\)	\(-\)	$+$	\(25\)
\(-\)	\(-\)	\(+\)	$+$	\(24\)
\(-\)	\(-\)	\(-\)	$-$	\(33\)
Plus space			\(+\)	\(104\)
Minus space			\(-\)	\(128\)

Trace form

\( 232 q + 4 q^{3} - 4 q^{5} + 8 q^{7} + 224 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\) 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	59
8024.2.a.a	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots\)
8024.2.a.b	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-3q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.c	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.d	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots\)
8024.2.a.e	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}-6q^{11}-4q^{13}+\cdots\)
8024.2.a.f	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}-2q^{9}+6q^{11}+\cdots\)
8024.2.a.g	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
8024.2.a.h	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
8024.2.a.i	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{9}+2q^{11}-6q^{13}-q^{17}+\cdots\)
8024.2.a.j	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+4q^{11}+2q^{13}+\cdots\)
8024.2.a.k	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
8024.2.a.l	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
8024.2.a.m	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
8024.2.a.n	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+3q^{7}+6q^{9}+2q^{11}+\cdots\)
8024.2.a.o	$8024$	$2$	8024.a	1.a	$1$	$1$	$1$	$64.072$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-q^{7}+6q^{9}-6q^{11}+\cdots\)
8024.2.a.p	$8024$	$2$	8024.a	1.a	$1$	$2$	$2$	$64.072$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
8024.2.a.q	$8024$	$2$	8024.a	1.a	$1$	$2$	$2$	$64.072$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
8024.2.a.r	$8024$	$2$	8024.a	1.a	$1$	$2$	$2$	$64.072$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta )q^{5}+\beta q^{7}-2q^{9}+\cdots\)
8024.2.a.s	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8024.2.a.t	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
8024.2.a.u	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}-2q^{9}+\cdots\)
8024.2.a.v	$8024$	$2$	8024.a	1.a	$1$	$18$	$18$	$64.072$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(2\)	\(11\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{6})q^{7}+\cdots\)
8024.2.a.w	$8024$	$2$	8024.a	1.a	$1$	$20$	$20$	$64.072$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(5\)		$-$	$-$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{17}q^{5}+\beta _{15}q^{7}+\beta _{2}q^{9}+\cdots\)
8024.2.a.x	$8024$	$2$	8024.a	1.a	$1$	$22$	$22$	$64.072$		None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8024.2.a.y	$8024$	$2$	8024.a	1.a	$1$	$23$	$23$	$64.072$		None	✓	$1$	$1$	\(0\)	\(-6\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8024.2.a.z	$8024$	$2$	8024.a	1.a	$1$	$24$	$24$	$64.072$		None	✓	$1$	$1$	\(0\)	\(-5\)	\(-7\)	\(-12\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8024.2.a.ba	$8024$	$2$	8024.a	1.a	$1$	$30$	$30$	$64.072$		None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8024.2.a.bb	$8024$	$2$	8024.a	1.a	$1$	$32$	$32$	$64.072$		None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8024.2.a.bc	$8024$	$2$	8024.a	1.a	$1$	$33$	$33$	$64.072$		None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4012))\)\(^{\oplus 2}\)