Space of modular forms of level 1840, weight 4, and trivial character

• Label: 1840.4.a
• Level: $1840$
• Weight: $4$
• Character orbit: 1840.a
• Rep. character: $\chi_{1840}(1,\cdot)$
• Character field: $\Q$
• Dimension: $132$
• Newform subspaces: $28$
• Sturm bound: $1152$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(1152\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1840))\).

	Total	New	Old
Modular forms	876	132	744
Cusp forms	852	132	720
Eisenstein series	24	0	24

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
\(+\)	\(+\)	\(+\)	\(+\)		\(112\)	\(18\)	\(94\)		\(109\)	\(18\)	\(91\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(109\)	\(15\)	\(94\)		\(106\)	\(15\)	\(91\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(107\)	\(15\)	\(92\)		\(104\)	\(15\)	\(89\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(110\)	\(18\)	\(92\)		\(107\)	\(18\)	\(89\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(107\)	\(18\)	\(89\)		\(104\)	\(18\)	\(86\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(110\)	\(15\)	\(95\)		\(107\)	\(15\)	\(92\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(112\)	\(18\)	\(94\)		\(109\)	\(18\)	\(91\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(109\)	\(15\)	\(94\)		\(106\)	\(15\)	\(91\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(444\)	\(69\)	\(375\)		\(432\)	\(69\)	\(363\)		\(12\)	\(0\)	\(12\)
Minus space			\(-\)		\(432\)	\(63\)	\(369\)		\(420\)	\(63\)	\(357\)		\(12\)	\(0\)	\(12\)

Trace form

132 * q + 12 * q^3 - 72 * q^7 + 1148 * q^9 + 152 * q^17 - 360 * q^19 - 138 * q^23 + 3300 * q^25 + 300 * q^27 + 480 * q^31 + 768 * q^33 + 420 * q^35 + 12 * q^39 + 40 * q^41 - 672 * q^43 - 940 * q^47 + 7188 * q^49 - 1712 * q^51 - 784 * q^53 - 440 * q^55 + 1104 * q^57 + 332 * q^59 - 400 * q^61 - 2552 * q^63 - 1512 * q^67 - 1864 * q^71 - 2088 * q^73 + 300 * q^75 + 368 * q^77 + 504 * q^79 + 8692 * q^81 + 2440 * q^83 - 60 * q^87 + 1880 * q^89 - 7816 * q^91 + 2136 * q^93 - 1520 * q^95 - 1512 * q^97 - 6424 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\) 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
1840.4.a.a	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				230.4.a.c	$1$	$0$	\(0\)	\(-7\)	\(5\)	\(-20\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+5q^{5}-20q^{7}+22q^{9}-6q^{11}+\cdots\)
1840.4.a.b	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				230.4.a.b	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}-3q^{7}-11q^{9}+2q^{11}+\cdots\)
1840.4.a.c	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				115.4.a.a	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(32\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}+2^{5}q^{7}-11q^{9}-40q^{11}+\cdots\)
1840.4.a.d	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				230.4.a.e	$1$	$0$	\(0\)	\(-1\)	\(-5\)	\(18\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-5q^{5}+18q^{7}-26q^{9}+2^{5}q^{11}+\cdots\)
1840.4.a.e	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				230.4.a.d	$1$	$0$	\(0\)	\(1\)	\(5\)	\(32\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{5}+2^{5}q^{7}-26q^{9}+30q^{11}+\cdots\)
1840.4.a.f	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				115.4.a.b	$1$	$1$	\(0\)	\(3\)	\(5\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+2q^{7}-18q^{9}+2^{4}q^{11}+\cdots\)
1840.4.a.g	$1840$	$4$	1840.a	1.a	$1$	$1$	$1$	$108.564$	\(\Q\)	None	✓				230.4.a.a	$1$	$1$	\(0\)	\(5\)	\(-5\)	\(-12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}-5q^{5}-12q^{7}-2q^{9}-22q^{11}+\cdots\)
1840.4.a.h	$1840$	$4$	1840.a	1.a	$1$	$2$	$2$	$108.564$	\(\Q(\sqrt{109}) \)	None	✓				115.4.a.c	$1$	$1$	\(0\)	\(3\)	\(10\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+5q^{5}+(2-5\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.4.a.i	$1840$	$4$	1840.a	1.a	$1$	$2$	$2$	$108.564$	\(\Q(\sqrt{73}) \)	None	✓				230.4.a.f	$1$	$1$	\(0\)	\(3\)	\(10\)	\(17\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+5q^{5}+(8+\beta )q^{7}+(-8+\cdots)q^{9}+\cdots\)
1840.4.a.j	$1840$	$4$	1840.a	1.a	$1$	$3$	$3$	$108.564$	3.3.318165.1	None	✓				230.4.a.g	$1$	$0$	\(0\)	\(1\)	\(15\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+5q^{5}+(-1-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
1840.4.a.k	$1840$	$4$	1840.a	1.a	$1$	$4$	$4$	$108.564$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.j	$1$	$1$	\(0\)	\(-14\)	\(20\)	\(-8\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{1})q^{3}+5q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.l	$1840$	$4$	1840.a	1.a	$1$	$4$	$4$	$108.564$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.i	$1$	$1$	\(0\)	\(-4\)	\(-20\)	\(-26\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}+(-6+\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.m	$1840$	$4$	1840.a	1.a	$1$	$4$	$4$	$108.564$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.h	$1$	$0$	\(0\)	\(4\)	\(-20\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.4.a.n	$1840$	$4$	1840.a	1.a	$1$	$5$	$5$	$108.564$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				115.4.a.e	$1$	$0$	\(0\)	\(-4\)	\(-25\)	\(3\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{4})q^{3}-5q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+\cdots\)
1840.4.a.o	$1840$	$4$	1840.a	1.a	$1$	$5$	$5$	$108.564$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				460.4.a.b	$1$	$0$	\(0\)	\(3\)	\(-25\)	\(-8\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
1840.4.a.p	$1840$	$4$	1840.a	1.a	$1$	$5$	$5$	$108.564$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				115.4.a.d	$1$	$1$	\(0\)	\(6\)	\(-25\)	\(15\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{3})q^{3}-5q^{5}+(2+3\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.q	$1840$	$4$	1840.a	1.a	$1$	$5$	$5$	$108.564$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				460.4.a.a	$1$	$0$	\(0\)	\(7\)	\(25\)	\(20\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{3}+5q^{5}+(5+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1840.4.a.r	$1840$	$4$	1840.a	1.a	$1$	$6$	$6$	$108.564$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		460.4.a.d	$1$	$1$	\(0\)	\(-3\)	\(-30\)	\(-20\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
1840.4.a.s	$1840$	$4$	1840.a	1.a	$1$	$6$	$6$	$108.564$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				920.4.a.b	$1$	$1$	\(0\)	\(-2\)	\(-30\)	\(-28\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-5q^{5}+(-5-\beta _{2}-\beta _{4})q^{7}+\cdots\)
1840.4.a.t	$1840$	$4$	1840.a	1.a	$1$	$6$	$6$	$108.564$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		460.4.a.c	$1$	$1$	\(0\)	\(1\)	\(30\)	\(-24\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+5q^{5}+(-4-\beta _{3}+\beta _{4})q^{7}+\cdots\)
1840.4.a.u	$1840$	$4$	1840.a	1.a	$1$	$6$	$6$	$108.564$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				920.4.a.a	$1$	$1$	\(0\)	\(4\)	\(30\)	\(14\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+5q^{5}+(2+\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1840.4.a.v	$1840$	$4$	1840.a	1.a	$1$	$8$	$8$	$108.564$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		115.4.a.f	$1$	$0$	\(0\)	\(0\)	\(40\)	\(-11\)		$-$	$-$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+5q^{5}+(-1+\beta _{3}+\beta _{6})q^{7}+\cdots\)
1840.4.a.w	$1840$	$4$	1840.a	1.a	$1$	$8$	$8$	$108.564$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				920.4.a.d	$1$	$0$	\(0\)	\(6\)	\(-40\)	\(3\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}-\beta _{5}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots\)
1840.4.a.x	$1840$	$4$	1840.a	1.a	$1$	$8$	$8$	$108.564$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				920.4.a.c	$1$	$0$	\(0\)	\(12\)	\(40\)	\(31\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+5q^{5}+(3+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1840.4.a.y	$1840$	$4$	1840.a	1.a	$1$	$9$	$9$	$108.564$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		920.4.a.f	$1$	$1$	\(0\)	\(-3\)	\(45\)	\(-25\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5q^{5}+(-3+\beta _{3})q^{7}+(7+\cdots)q^{9}+\cdots\)
1840.4.a.z	$1840$	$4$	1840.a	1.a	$1$	$9$	$9$	$108.564$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		920.4.a.e	$1$	$1$	\(0\)	\(3\)	\(-45\)	\(-25\)		$+$	$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5q^{5}+(-3+\beta _{3})q^{7}+(6+\cdots)q^{9}+\cdots\)
1840.4.a.ba	$1840$	$4$	1840.a	1.a	$1$	$10$	$10$	$108.564$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		920.4.a.h	$1$	$0$	\(0\)	\(-5\)	\(50\)	\(-14\)		$+$	$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5q^{5}+(-1-\beta _{1}+\beta _{6})q^{7}+\cdots\)
1840.4.a.bb	$1840$	$4$	1840.a	1.a	$1$	$10$	$10$	$108.564$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		920.4.a.g	$1$	$0$	\(0\)	\(1\)	\(-50\)	\(-28\)		$+$	$+$	$+$	$+$	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5q^{5}+(-3-\beta _{1}-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1840))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1840)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)