Space of modular forms of level 1150, weight 4, and trivial character

• Label: 1150.4.a
• Level: $1150$
• Weight: $4$
• Character orbit: 1150.a
• Rep. character: $\chi_{1150}(1,\cdot)$
• Character field: $\Q$
• Dimension: $104$
• Newform subspaces: $28$
• Sturm bound: $720$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(720\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1150))\).

	Total	New	Old
Modular forms	552	104	448
Cusp forms	528	104	424
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
\(+\)	\(+\)	\(+\)	\(+\)		\(75\)	\(12\)	\(63\)		\(72\)	\(12\)	\(60\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(63\)	\(11\)	\(52\)		\(60\)	\(11\)	\(49\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(64\)	\(13\)	\(51\)		\(61\)	\(13\)	\(48\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(74\)	\(15\)	\(59\)		\(71\)	\(15\)	\(56\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(72\)	\(13\)	\(59\)		\(69\)	\(13\)	\(56\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(66\)	\(14\)	\(52\)		\(63\)	\(14\)	\(49\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(65\)	\(14\)	\(51\)		\(62\)	\(14\)	\(48\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(73\)	\(12\)	\(61\)		\(70\)	\(12\)	\(58\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(280\)	\(55\)	\(225\)		\(268\)	\(55\)	\(213\)		\(12\)	\(0\)	\(12\)
Minus space			\(-\)		\(272\)	\(49\)	\(223\)		\(260\)	\(49\)	\(211\)		\(12\)	\(0\)	\(12\)

Trace form

104 * q + 4 * q^2 - 8 * q^3 + 416 * q^4 - 32 * q^6 - 16 * q^7 + 16 * q^8 + 864 * q^9 - 66 * q^11 - 32 * q^12 - 36 * q^13 + 40 * q^14 + 1664 * q^16 - 96 * q^17 + 52 * q^18 + 182 * q^19 + 380 * q^21 + 148 * q^22 - 128 * q^24 + 248 * q^26 - 428 * q^27 - 64 * q^28 + 256 * q^29 + 76 * q^31 + 64 * q^32 - 716 * q^33 + 120 * q^34 + 3456 * q^36 - 494 * q^37 - 484 * q^38 - 396 * q^39 - 604 * q^41 + 64 * q^42 - 366 * q^43 - 264 * q^44 - 92 * q^46 - 452 * q^47 - 128 * q^48 + 3344 * q^49 + 1808 * q^51 - 144 * q^52 + 182 * q^53 + 568 * q^54 + 160 * q^56 - 256 * q^57 - 64 * q^58 + 384 * q^59 - 3098 * q^61 + 1136 * q^62 + 748 * q^63 + 6656 * q^64 + 1016 * q^66 - 2006 * q^67 - 384 * q^68 - 276 * q^69 + 2028 * q^71 + 208 * q^72 + 1040 * q^73 - 1460 * q^74 + 728 * q^76 + 1496 * q^77 + 2800 * q^78 - 1308 * q^79 + 9176 * q^81 - 656 * q^82 + 1090 * q^83 + 1520 * q^84 - 980 * q^86 + 6212 * q^87 + 592 * q^88 + 44 * q^89 - 2124 * q^91 + 1828 * q^93 - 1328 * q^94 - 512 * q^96 + 464 * q^97 - 28 * q^98 - 3746 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1150))\) 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
1150.4.a.a	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓	✓			1150.4.a.a	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(-21\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-21q^{7}+\cdots\)
1150.4.a.b	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				230.4.a.e	$1$	$1$	\(-2\)	\(-1\)	\(0\)	\(18\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+4q^{4}+2q^{6}+18q^{7}+\cdots\)
1150.4.a.c	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				230.4.a.d	$1$	$0$	\(-2\)	\(1\)	\(0\)	\(32\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+4q^{4}-2q^{6}+2^{5}q^{7}+\cdots\)
1150.4.a.d	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				46.4.a.b	$1$	$1$	\(-2\)	\(9\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+9q^{3}+4q^{4}-18q^{6}-2q^{7}+\cdots\)
1150.4.a.e	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				230.4.a.c	$1$	$1$	\(2\)	\(-7\)	\(0\)	\(-20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-7q^{3}+4q^{4}-14q^{6}-20q^{7}+\cdots\)
1150.4.a.f	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				230.4.a.b	$1$	$1$	\(2\)	\(-4\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}+4q^{4}-8q^{6}-3q^{7}+\cdots\)
1150.4.a.g	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				46.4.a.a	$1$	$1$	\(2\)	\(1\)	\(0\)	\(12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+4q^{4}+2q^{6}+12q^{7}+\cdots\)
1150.4.a.h	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓	✓			1150.4.a.a	$1$	$0$	\(2\)	\(2\)	\(0\)	\(21\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+21q^{7}+\cdots\)
1150.4.a.i	$1150$	$4$	1150.a	1.a	$1$	$1$	$1$	$67.852$	\(\Q\)	None	✓				230.4.a.a	$1$	$1$	\(2\)	\(5\)	\(0\)	\(-12\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+5q^{3}+4q^{4}+10q^{6}-12q^{7}+\cdots\)
1150.4.a.j	$1150$	$4$	1150.a	1.a	$1$	$2$	$2$	$67.852$	\(\Q(\sqrt{73}) \)	None	✓				46.4.a.d	$1$	$0$	\(-4\)	\(-3\)	\(0\)	\(-12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+(2+2\beta )q^{6}+\cdots\)
1150.4.a.k	$1150$	$4$	1150.a	1.a	$1$	$2$	$2$	$67.852$	\(\Q(\sqrt{41}) \)	None	✓				46.4.a.c	$1$	$0$	\(4\)	\(1\)	\(0\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.l	$1150$	$4$	1150.a	1.a	$1$	$2$	$2$	$67.852$	\(\Q(\sqrt{73}) \)	None	✓				230.4.a.f	$1$	$0$	\(4\)	\(3\)	\(0\)	\(17\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(2+2\beta )q^{6}+\cdots\)
1150.4.a.m	$1150$	$4$	1150.a	1.a	$1$	$3$	$3$	$67.852$	3.3.318165.1	None	✓				230.4.a.g	$1$	$1$	\(6\)	\(1\)	\(0\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1150.4.a.n	$1150$	$4$	1150.a	1.a	$1$	$4$	$4$	$67.852$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.j	$1$	$1$	\(-8\)	\(-14\)	\(0\)	\(-8\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-4+\beta _{1})q^{3}+4q^{4}+(8-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.o	$1150$	$4$	1150.a	1.a	$1$	$4$	$4$	$67.852$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.i	$1$	$0$	\(-8\)	\(-4\)	\(0\)	\(-26\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.p	$1150$	$4$	1150.a	1.a	$1$	$4$	$4$	$67.852$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				230.4.a.h	$1$	$0$	\(8\)	\(4\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.q	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1150.4.a.q	$1$	$1$	\(-10\)	\(-5\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.r	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		1150.4.a.r	$1$	$1$	\(-10\)	\(0\)	\(0\)	\(-20\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-4+\cdots)q^{7}+\cdots\)
1150.4.a.s	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		1150.4.a.s	$1$	$0$	\(-10\)	\(12\)	\(0\)	\(-24\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(-4-2\beta _{2}+\cdots)q^{6}+\cdots\)
1150.4.a.t	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1150.4.a.s	$1$	$1$	\(10\)	\(-12\)	\(0\)	\(24\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2-\beta _{2})q^{3}+4q^{4}+(-4+\cdots)q^{6}+\cdots\)
1150.4.a.u	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1150.4.a.r	$1$	$0$	\(10\)	\(0\)	\(0\)	\(20\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(4+\cdots)q^{7}+\cdots\)
1150.4.a.v	$1150$	$4$	1150.a	1.a	$1$	$5$	$5$	$67.852$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓		1150.4.a.q	$1$	$0$	\(10\)	\(5\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.w	$1150$	$4$	1150.a	1.a	$1$	$6$	$6$	$67.852$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1150.4.a.w	$1$	$0$	\(-12\)	\(5\)	\(0\)	\(42\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.x	$1150$	$4$	1150.a	1.a	$1$	$6$	$6$	$67.852$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		1150.4.a.w	$1$	$1$	\(12\)	\(-5\)	\(0\)	\(-42\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.y	$1150$	$4$	1150.a	1.a	$1$	$7$	$7$	$67.852$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		230.4.b.a	$1$	$1$	\(-14\)	\(9\)	\(0\)	\(44\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(-2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.z	$1150$	$4$	1150.a	1.a	$1$	$7$	$7$	$67.852$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		230.4.b.a	$1$	$1$	\(14\)	\(-9\)	\(0\)	\(-44\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.ba	$1150$	$4$	1150.a	1.a	$1$	$9$	$9$	$67.852$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		230.4.b.b	$1$	$0$	\(-18\)	\(-3\)	\(0\)	\(-44\)		$+$	$-$	$-$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-5+\cdots)q^{7}+\cdots\)
1150.4.a.bb	$1150$	$4$	1150.a	1.a	$1$	$9$	$9$	$67.852$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		230.4.b.b	$1$	$0$	\(18\)	\(3\)	\(0\)	\(44\)		$-$	$-$	$+$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(5+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1150))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1150)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)