Space of modular forms of level 2888, weight 2, and trivial character

• Label: 2888.2.a
• Level: $2888$
• Weight: $2$
• Character orbit: 2888.a
• Rep. character: $\chi_{2888}(1,\cdot)$
• Character field: $\Q$
• Dimension: $85$
• Newform subspaces: $25$
• Sturm bound: $760$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2888.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(760\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2888))\).

	Total	New	Old
Modular forms	420	85	335
Cusp forms	341	85	256
Eisenstein series	79	0	79

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

\(2\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(18\)
\(+\)	\(-\)	$-$	\(25\)
\(-\)	\(+\)	$-$	\(22\)
\(-\)	\(-\)	$+$	\(20\)
Plus space		\(+\)	\(38\)
Minus space		\(-\)	\(47\)

Trace form

\( 85 q - 4 q^{7} + 79 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\) 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	19
2888.2.a.a	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
2888.2.a.b	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
2888.2.a.c	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
2888.2.a.d	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
2888.2.a.e	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{9}-4q^{11}-5q^{13}+\cdots\)
2888.2.a.f	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
2888.2.a.g	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(5\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.h	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.i	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.j	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
2888.2.a.k	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
2888.2.a.l	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(5\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots\)
2888.2.a.m	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.n	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.o	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.961.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2888.2.a.p	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.q	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.r	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2888.2.a.s	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
2888.2.a.t	$2888$	$2$	2888.a	1.a	$1$	$6$	$6$	$23.061$	6.6.3022625.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-2\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.u	$2888$	$2$	2888.a	1.a	$1$	$6$	$6$	$23.061$	6.6.3022625.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2888.2.a.v	$2888$	$2$	2888.a	1.a	$1$	$8$	$8$	$23.061$	8.8.\(\cdots\).1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.w	$2888$	$2$	2888.a	1.a	$1$	$8$	$8$	$23.061$	8.8.\(\cdots\).1	None	✓	$1$	$0$	\(0\)	\(6\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
2888.2.a.x	$2888$	$2$	2888.a	1.a	$1$	$9$	$9$	$23.061$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
2888.2.a.y	$2888$	$2$	2888.a	1.a	$1$	$9$	$9$	$23.061$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 2}\)