Space of modular forms of level 2952, weight 2, and trivial character

• Label: 2952.2.a
• Level: $2952$
• Weight: $2$
• Character orbit: 2952.a
• Rep. character: $\chi_{2952}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $20$
• Sturm bound: $1008$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2952 = 2^{3} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2952.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1008\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2952))\).

	Total	New	Old
Modular forms	520	50	470
Cusp forms	489	50	439
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
Plus space			\(+\)	\(22\)
Minus space			\(-\)	\(28\)

Trace form

\( 50 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2952))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	41
2952.2.a.a	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓	✓			2952.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-3q^{13}-5q^{17}+3q^{19}+\cdots\)
2952.2.a.b	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				328.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-2q^{11}+6q^{13}+6q^{17}+\cdots\)
2952.2.a.c	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				984.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-5q^{11}+3q^{17}-2q^{19}+\cdots\)
2952.2.a.d	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				984.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+3q^{11}-6q^{13}+7q^{17}-2q^{23}+\cdots\)
2952.2.a.e	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				984.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{11}-3q^{13}+3q^{17}+\cdots\)
2952.2.a.f	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				328.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
2952.2.a.g	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓				984.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{11}+4q^{13}+7q^{17}+2q^{19}+\cdots\)
2952.2.a.h	$2952$	$2$	2952.a	1.a	$1$	$1$	$1$	$23.572$	\(\Q\)	None	✓	✓			2952.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}-3q^{13}+5q^{17}+3q^{19}+\cdots\)
2952.2.a.i	$2952$	$2$	2952.a	1.a	$1$	$2$	$2$	$23.572$	\(\Q(\sqrt{3}) \)	None	✓				328.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta )q^{7}+(-3+\beta )q^{11}-2q^{17}+\cdots\)
2952.2.a.j	$2952$	$2$	2952.a	1.a	$1$	$2$	$2$	$23.572$	\(\Q(\sqrt{2}) \)	None	✓				984.2.a.e	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+(-2+\beta )q^{7}+(-1-3\beta )q^{11}+\cdots\)
2952.2.a.k	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.1436.1	None	✓		✓		984.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2952.2.a.l	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.788.1	None	✓		✓		328.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2952.2.a.m	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.961.1	None	✓				984.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+2q^{7}+(1-\beta _{1}+\beta _{2})q^{11}+\cdots\)
2952.2.a.n	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.892.1	None	✓				984.2.a.f	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots\)
2952.2.a.o	$2952$	$2$	2952.a	1.a	$1$	$3$	$3$	$23.572$	3.3.148.1	None	✓				328.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{1}+2\beta _{2})q^{7}+\cdots\)
2952.2.a.p	$2952$	$2$	2952.a	1.a	$1$	$4$	$4$	$23.572$	4.4.20308.1	None	✓	✓	✓	✓	2952.2.a.p	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
2952.2.a.q	$2952$	$2$	2952.a	1.a	$1$	$4$	$4$	$23.572$	4.4.20308.1	None	✓	✓	✓	✓	2952.2.a.p	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
2952.2.a.r	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.40129248.1	None	✓	✓	✓		2952.2.a.r	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(2+\beta _{4})q^{11}+\cdots\)
2952.2.a.s	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.3858104.1	None	✓		✓		984.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
2952.2.a.t	$2952$	$2$	2952.a	1.a	$1$	$5$	$5$	$23.572$	5.5.40129248.1	None	✓	✓	✓		2952.2.a.r	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+\beta _{3}q^{7}+(-2-\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2952)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(492))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(738))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1476))\)\(^{\oplus 2}\)