Space of modular forms of level 1848, weight 2, and trivial character

• Label: 1848.2.a
• Level: $1848$
• Weight: $2$
• Character orbit: 1848.a
• Rep. character: $\chi_{1848}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $21$
• Sturm bound: $768$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(768\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1848))\).

	Total	New	Old
Modular forms	400	32	368
Cusp forms	369	32	337
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.

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(1\)
Plus space				\(+\)	\(14\)
Minus space				\(-\)	\(18\)

Trace form

\( 32 q - 8 q^{5} + 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\) 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	3	7	11
1848.2.a.a	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
1848.2.a.b	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
1848.2.a.c	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots\)
1848.2.a.d	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
1848.2.a.e	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.f	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
1848.2.a.g	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.h	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1848.2.a.i	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.j	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.k	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
1848.2.a.l	$1848$	$2$	1848.a	1.a	$1$	$1$	$1$	$14.756$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
1848.2.a.m	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.n	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.o	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.p	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
1848.2.a.q	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.r	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.s	$1848$	$2$	1848.a	1.a	$1$	$2$	$2$	$14.756$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
1848.2.a.t	$1848$	$2$	1848.a	1.a	$1$	$3$	$3$	$14.756$	3.3.961.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1848.2.a.u	$1848$	$2$	1848.a	1.a	$1$	$3$	$3$	$14.756$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+q^{11}+\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1848))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1848)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 2}\)