Space of modular forms of level 1840, weight 2, and trivial character

• Label: 1840.2.a
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.a
• Rep. character: $\chi_{1840}(1,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $22$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1840))\).

	Total	New	Old
Modular forms	300	44	256
Cusp forms	277	44	233
Eisenstein series	23	0	23

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

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(35\)	\(4\)	\(31\)		\(33\)	\(4\)	\(29\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(38\)	\(7\)	\(31\)		\(35\)	\(7\)	\(28\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(40\)	\(7\)	\(33\)		\(37\)	\(7\)	\(30\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(37\)	\(4\)	\(33\)		\(34\)	\(4\)	\(30\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(40\)	\(4\)	\(36\)		\(37\)	\(4\)	\(33\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(37\)	\(7\)	\(30\)		\(34\)	\(7\)	\(27\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(35\)	\(4\)	\(31\)		\(32\)	\(4\)	\(28\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(38\)	\(7\)	\(31\)		\(35\)	\(7\)	\(28\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(144\)	\(19\)	\(125\)		\(133\)	\(19\)	\(114\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(156\)	\(25\)	\(131\)		\(144\)	\(25\)	\(119\)		\(12\)	\(0\)	\(12\)

Trace form

44 * q - 4 * q^3 - 8 * q^7 + 52 * q^9 + 8 * q^17 - 8 * q^19 + 6 * q^23 + 44 * q^25 - 4 * q^27 - 32 * q^31 - 12 * q^35 - 20 * q^39 - 8 * q^41 - 32 * q^43 + 20 * q^47 + 28 * q^49 + 16 * q^51 + 16 * q^53 + 8 * q^55 - 16 * q^57 + 28 * q^59 + 16 * q^61 + 8 * q^63 - 8 * q^67 - 8 * q^71 + 8 * q^73 - 4 * q^75 + 16 * q^77 - 8 * q^79 + 60 * q^81 + 40 * q^83 + 36 * q^87 + 8 * q^89 + 24 * q^91 - 24 * q^93 + 16 * q^95 + 8 * q^97 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\) 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	5	23
1840.2.a.a	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				460.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}-2q^{7}+6q^{9}-3q^{13}+\cdots\)
1840.2.a.b	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				920.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{13}+q^{15}+\cdots\)
1840.2.a.c	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				460.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}-2q^{9}+6q^{11}+\cdots\)
1840.2.a.d	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				115.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
1840.2.a.e	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				460.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-6q^{11}+6q^{13}+\cdots\)
1840.2.a.f	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				920.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
1840.2.a.g	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				920.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-2q^{11}-5q^{13}+\cdots\)
1840.2.a.h	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				460.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1840.2.a.i	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	\(\Q\)	None	✓				920.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+2q^{7}+6q^{9}+q^{13}+\cdots\)
1840.2.a.j	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{13}) \)	None	✓				230.2.a.b	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots\)
1840.2.a.k	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}-2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
1840.2.a.l	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{5}) \)	None	✓				230.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1840.2.a.m	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{17}) \)	None	✓				460.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.n	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{21}) \)	None	✓		✓		230.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
1840.2.a.o	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.p	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	\(\Q(\sqrt{5}) \)	None	✓				115.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots\)
1840.2.a.q	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.229.1	None	✓		✓		920.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
1840.2.a.r	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.1101.1	None	✓		✓		230.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
1840.2.a.s	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.2597.1	None	✓		✓		920.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
1840.2.a.t	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.621.1	None	✓		✓		920.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1840.2.a.u	$1840$	$2$	1840.a	1.a	$1$	$4$	$4$	$14.692$	4.4.15317.1	None	✓		✓		115.2.a.c	$1$	$0$	\(0\)	\(2\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+(1+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
1840.2.a.v	$1840$	$2$	1840.a	1.a	$1$	$5$	$5$	$14.692$	5.5.13955077.1	None	✓		✓		920.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1840)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)