Space of modular forms of level 2832, weight 2, and trivial character

• Label: 2832.2.a
• Level: $2832$
• Weight: $2$
• Character orbit: 2832.a
• Rep. character: $\chi_{2832}(1,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $25$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2832 = 2^{4} \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2832.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2832))\).

	Total	New	Old
Modular forms	492	58	434
Cusp forms	469	58	411
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.

\(2\)	\(3\)	\(59\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(-\)	\(+\)	\(-\)	$+$	\(7\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(8\)
Plus space			\(+\)	\(27\)
Minus space			\(-\)	\(31\)

Trace form

\( 58 q - 2 q^{3} + 4 q^{5} + 58 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2832))\) 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	59
2832.2.a.a	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
2832.2.a.b	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
2832.2.a.c	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
2832.2.a.d	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}+4q^{13}+6q^{17}+\cdots\)
2832.2.a.e	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+5q^{11}+q^{13}+q^{17}+\cdots\)
2832.2.a.f	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
2832.2.a.g	$2832$	$2$	2832.a	1.a	$1$	$1$	$1$	$22.614$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{15}+\cdots\)
2832.2.a.h	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-6\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+(3+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2832.2.a.i	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-2\beta )q^{5}+(2-3\beta )q^{7}+\cdots\)
2832.2.a.j	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
2832.2.a.k	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(3-2\beta )q^{11}+\cdots\)
2832.2.a.l	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{11}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2832.2.a.m	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
2832.2.a.n	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
2832.2.a.o	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-2\beta )q^{5}+(4-\beta )q^{7}+q^{9}+\cdots\)
2832.2.a.p	$2832$	$2$	2832.a	1.a	$1$	$2$	$2$	$22.614$	\(\Q(\sqrt{61}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(6\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+\beta q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
2832.2.a.q	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.733.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)
2832.2.a.r	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2832.2.a.s	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
2832.2.a.t	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-9\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
2832.2.a.u	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.621.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
2832.2.a.v	$2832$	$2$	2832.a	1.a	$1$	$3$	$3$	$22.614$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2832.2.a.w	$2832$	$2$	2832.a	1.a	$1$	$4$	$4$	$22.614$	4.4.27004.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2832.2.a.x	$2832$	$2$	2832.a	1.a	$1$	$5$	$5$	$22.614$	5.5.5755900.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots\)
2832.2.a.y	$2832$	$2$	2832.a	1.a	$1$	$6$	$6$	$22.614$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(6\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2832))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2832)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(354))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(472))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(708))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(944))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1416))\)\(^{\oplus 2}\)