Space of modular forms of level 1935, weight 2, and trivial character

• Label: 1935.2.a
• Level: $1935$
• Weight: $2$
• Character orbit: 1935.a
• Rep. character: $\chi_{1935}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $26$
• Sturm bound: $528$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1935 = 3^{2} \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1935.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(528\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1935))\).

	Total	New	Old
Modular forms	272	70	202
Cusp forms	257	70	187
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.

\(3\)	\(5\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(15\)
Plus space			\(+\)	\(28\)
Minus space			\(-\)	\(42\)

Trace form

\( 70 q + 74 q^{4} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1935))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	43
1935.2.a.a	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.f	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots\)
1935.2.a.b	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓	✓			1935.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots\)
1935.2.a.c	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓	✓			1935.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
1935.2.a.d	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
1935.2.a.e	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots\)
1935.2.a.f	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-2q^{7}+5q^{11}-5q^{13}+\cdots\)
1935.2.a.g	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				215.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-2q^{7}+q^{11}-q^{13}+\cdots\)
1935.2.a.h	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓	✓			1935.2.a.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
1935.2.a.i	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓	✓			1935.2.a.c	$1$	$0$	\(1\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
1935.2.a.j	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-4q^{7}-2q^{10}+\cdots\)
1935.2.a.k	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	\(\Q\)	None	✓				645.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+4q^{7}-2q^{10}+\cdots\)
1935.2.a.l	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	\(\Q(\sqrt{2}) \)	None	✓				645.2.a.g	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}-\beta q^{7}-2\beta q^{8}+\beta q^{10}+\cdots\)
1935.2.a.m	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	\(\Q(\sqrt{6}) \)	None	✓	✓			1935.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}-q^{5}+(-2-\beta )q^{7}+\cdots\)
1935.2.a.n	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	\(\Q(\sqrt{6}) \)	None	✓	✓			1935.2.a.m	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}+q^{5}+(-2+\beta )q^{7}+\cdots\)
1935.2.a.o	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.316.1	None	✓		✓		645.2.a.j	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1935.2.a.p	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.148.1	None	✓				645.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
1935.2.a.q	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.148.1	None	✓				645.2.a.h	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1935.2.a.r	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.321.1	None	✓				215.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
1935.2.a.s	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.230224.1	None	✓	✓	✓	✓	1935.2.a.s	$1$	$1$	\(-3\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1935.2.a.t	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.220036.1	None	✓		✓		645.2.a.l	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
1935.2.a.u	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1933097.1	None	✓		✓		215.2.a.c	$1$	$0$	\(-2\)	\(0\)	\(-5\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
1935.2.a.v	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1240016.1	None	✓	✓	✓		1935.2.a.v	$1$	$1$	\(-1\)	\(0\)	\(-5\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
1935.2.a.w	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1240016.1	None	✓	✓	✓		1935.2.a.v	$1$	$0$	\(1\)	\(0\)	\(5\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
1935.2.a.x	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.230224.1	None	✓	✓	✓	✓	1935.2.a.s	$1$	$0$	\(3\)	\(0\)	\(-5\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
1935.2.a.y	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.135076.1	None	✓				645.2.a.k	$1$	$0$	\(4\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+(3-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
1935.2.a.z	$1935$	$2$	1935.a	1.a	$1$	$6$	$6$	$15.451$	6.6.32503921.1	None	✓		✓		215.2.a.d	$1$	$0$	\(-3\)	\(0\)	\(6\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1935))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1935)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(645))\)\(^{\oplus 2}\)