Space of modular forms of level 1960, weight 4, and trivial character

• Label: 1960.4.a
• Level: $1960$
• Weight: $4$
• Character orbit: 1960.a
• Rep. character: $\chi_{1960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $123$
• Newform subspaces: $32$
• Sturm bound: $1344$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(1344\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1960))\).

	Total	New	Old
Modular forms	1040	123	917
Cusp forms	976	123	853
Eisenstein series	64	0	64

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

\(2\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(15\)
\(+\)	\(+\)	\(-\)	$-$	\(15\)
\(+\)	\(-\)	\(+\)	$-$	\(13\)
\(+\)	\(-\)	\(-\)	$+$	\(18\)
\(-\)	\(+\)	\(+\)	$-$	\(16\)
\(-\)	\(+\)	\(-\)	$+$	\(15\)
\(-\)	\(-\)	\(+\)	$+$	\(16\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(64\)
Minus space			\(-\)	\(59\)

Trace form

\( 123 q - 4 q^{3} + 5 q^{5} + 1123 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1960))\) 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	5	7
1960.4.a.a	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-10\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-10q^{3}+5q^{5}+73q^{9}-2^{4}q^{11}+\cdots\)
1960.4.a.b	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}-5q^{5}+22q^{9}+9q^{11}-23q^{13}+\cdots\)
1960.4.a.c	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-7\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+5q^{5}+22q^{9}+58q^{11}-82q^{13}+\cdots\)
1960.4.a.d	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}+5q^{5}-2q^{9}-39q^{11}+19q^{13}+\cdots\)
1960.4.a.e	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}-11q^{9}+6^{2}q^{11}+42q^{13}+\cdots\)
1960.4.a.f	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-5q^{5}-26q^{9}-39q^{11}+17q^{13}+\cdots\)
1960.4.a.g	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(4\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-5q^{5}-11q^{9}+20q^{11}+10q^{13}+\cdots\)
1960.4.a.h	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(6\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{3}+5q^{5}+9q^{9}+2^{4}q^{11}-58q^{13}+\cdots\)
1960.4.a.i	$1960$	$4$	1960.a	1.a	$1$	$1$	$1$	$115.644$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(-5\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-5q^{5}+22q^{9}+58q^{11}+82q^{13}+\cdots\)
1960.4.a.j	$1960$	$4$	1960.a	1.a	$1$	$2$	$2$	$115.644$	\(\Q(\sqrt{669}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+5q^{5}-26q^{9}+(13+\beta )q^{11}+\cdots\)
1960.4.a.k	$1960$	$4$	1960.a	1.a	$1$	$2$	$2$	$115.644$	\(\Q(\sqrt{249}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+5q^{5}+(35+\beta )q^{9}+(-2+\beta )q^{11}+\cdots\)
1960.4.a.l	$1960$	$4$	1960.a	1.a	$1$	$2$	$2$	$115.644$	\(\Q(\sqrt{249}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-5q^{5}+(35+\beta )q^{9}+(-2+\beta )q^{11}+\cdots\)
1960.4.a.m	$1960$	$4$	1960.a	1.a	$1$	$2$	$2$	$115.644$	\(\Q(\sqrt{669}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-10\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-5q^{5}-26q^{9}+(13-\beta )q^{11}+\cdots\)
1960.4.a.n	$1960$	$4$	1960.a	1.a	$1$	$2$	$2$	$115.644$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(10\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+5q^{5}+(-8+3\beta )q^{9}+\cdots\)
1960.4.a.o	$1960$	$4$	1960.a	1.a	$1$	$3$	$3$	$115.644$	3.3.78693.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-15\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}+(20-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.4.a.p	$1960$	$4$	1960.a	1.a	$1$	$3$	$3$	$115.644$	3.3.6053.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(15\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+5q^{5}+(13-\beta _{1}+3\beta _{2})q^{9}+\cdots\)
1960.4.a.q	$1960$	$4$	1960.a	1.a	$1$	$3$	$3$	$115.644$	3.3.11853.1	None	✓	$1$	$1$	\(0\)	\(6\)	\(-15\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}-5q^{5}+(3-6\beta _{1}+\beta _{2})q^{9}+\cdots\)
1960.4.a.r	$1960$	$4$	1960.a	1.a	$1$	$3$	$3$	$115.644$	3.3.11045.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(15\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+5q^{5}+(8-7\beta _{1}+\beta _{2})q^{9}+\cdots\)
1960.4.a.s	$1960$	$4$	1960.a	1.a	$1$	$5$	$5$	$115.644$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-25\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-5q^{5}+(4-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.4.a.t	$1960$	$4$	1960.a	1.a	$1$	$5$	$5$	$115.644$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-25\)	\(0\)		$+$	$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}+(19-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.4.a.u	$1960$	$4$	1960.a	1.a	$1$	$5$	$5$	$115.644$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(25\)	\(0\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+5q^{5}+(19-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.4.a.v	$1960$	$4$	1960.a	1.a	$1$	$5$	$5$	$115.644$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(6\)	\(25\)	\(0\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+5q^{5}+(4-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.4.a.w	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8\)	\(-30\)	\(0\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-5q^{5}+(6+\beta _{1}-\beta _{3}+\cdots)q^{9}+\cdots\)
1960.4.a.x	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(30\)	\(0\)		$-$	$-$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+5q^{5}+(6+4\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.4.a.y	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-30\)	\(0\)		$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5q^{5}+(15+\beta _{1}+\beta _{3})q^{9}+\cdots\)
1960.4.a.z	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(30\)	\(0\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5q^{5}+(15+\beta _{1}+\beta _{3})q^{9}+\cdots\)
1960.4.a.ba	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(7\)	\(-30\)	\(0\)		$-$	$+$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-5q^{5}+(6+4\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.4.a.bb	$1960$	$4$	1960.a	1.a	$1$	$6$	$6$	$115.644$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(30\)	\(0\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+5q^{5}+(6+\beta _{1}-\beta _{3}+\cdots)q^{9}+\cdots\)
1960.4.a.bc	$1960$	$4$	1960.a	1.a	$1$	$8$	$8$	$115.644$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(40\)	\(0\)		$+$	$-$	$+$	$-$	$2^{6}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+5q^{5}+(7+2\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
1960.4.a.bd	$1960$	$4$	1960.a	1.a	$1$	$8$	$8$	$115.644$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-40\)	\(0\)		$+$	$+$	$+$	$+$	$2^{6}\cdot 7$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}+(7+2\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
1960.4.a.be	$1960$	$4$	1960.a	1.a	$1$	$10$	$10$	$115.644$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-50\)	\(0\)		$-$	$+$	$+$	$-$	$2^{9}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-5q^{5}+(12+2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.4.a.bf	$1960$	$4$	1960.a	1.a	$1$	$10$	$10$	$115.644$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(50\)	\(0\)		$-$	$-$	$+$	$+$	$2^{9}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+5q^{5}+(12+2\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1960))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1960)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)