Space of modular forms of level 1862, weight 2, and trivial character

• Label: 1862.2.a
• Level: $1862$
• Weight: $2$
• Character orbit: 1862.a
• Rep. character: $\chi_{1862}(1,\cdot)$
• Character field: $\Q$
• Dimension: $61$
• Newform subspaces: $24$
• Sturm bound: $560$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1862.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(560\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1862))\).

	Total	New	Old
Modular forms	296	61	235
Cusp forms	265	61	204
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.

\(2\)	\(7\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(+\)	\(-\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	$-$	\(10\)
\(+\)	\(-\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(-\)	$-$	\(11\)
Plus space			\(+\)	\(23\)
Minus space			\(-\)	\(38\)

Trace form

\( 61 q - q^{2} - 4 q^{3} + 61 q^{4} - 2 q^{5} + 6 q^{6} - q^{8} + 67 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\) 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	7	19
1862.2.a.a	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(-2\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{8}+\cdots\)
1862.2.a.b	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
1862.2.a.c	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{8}+\cdots\)
1862.2.a.d	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
1862.2.a.e	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
1862.2.a.f	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
1862.2.a.g	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+3\beta )q^{5}+\cdots\)
1862.2.a.h	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{29}) \)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
1862.2.a.i	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
1862.2.a.j	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
1862.2.a.k	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-3\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1862.2.a.l	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(2\)	\(-1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
1862.2.a.m	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(2\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\)
1862.2.a.n	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.257.1	None	✓	$1$	$0$	\(-3\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
1862.2.a.o	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$1$	\(-3\)	\(-1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
1862.2.a.p	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$0$	\(-3\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1862.2.a.q	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.257.1	None	✓	$1$	$0$	\(-3\)	\(2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
1862.2.a.r	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(-5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
1862.2.a.s	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.9792.1	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
1862.2.a.t	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.9792.1	None	✓	$1$	$0$	\(-4\)	\(2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1862.2.a.u	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.2624.1	None	✓	$1$	$1$	\(4\)	\(-6\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-2+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1862.2.a.v	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.2624.1	None	✓	$1$	$0$	\(4\)	\(6\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1862.2.a.w	$1862$	$2$	1862.a	1.a	$1$	$5$	$5$	$14.868$	5.5.6530556.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1862.2.a.x	$1862$	$2$	1862.a	1.a	$1$	$5$	$5$	$14.868$	5.5.6530556.1	None	✓	$1$	$0$	\(5\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1862))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1862)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 2}\)