Space of modular forms of level 1911, weight 4, and trivial character

• Label: 1911.4.a
• Level: $1911$
• Weight: $4$
• Character orbit: 1911.a
• Rep. character: $\chi_{1911}(1,\cdot)$
• Character field: $\Q$
• Dimension: $246$
• Newform subspaces: $33$
• Sturm bound: $1045$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 33 \)
Sturm bound:			\(1045\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1911))\).

	Total	New	Old
Modular forms	800	246	554
Cusp forms	768	246	522
Eisenstein series	32	0	32

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

\(3\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(105\)	\(33\)	\(72\)		\(101\)	\(33\)	\(68\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)		\(97\)	\(27\)	\(70\)		\(93\)	\(27\)	\(66\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(95\)	\(30\)	\(65\)		\(91\)	\(30\)	\(61\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(103\)	\(33\)	\(70\)		\(99\)	\(33\)	\(66\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(95\)	\(25\)	\(70\)		\(91\)	\(25\)	\(66\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(103\)	\(35\)	\(68\)		\(99\)	\(35\)	\(64\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(105\)	\(36\)	\(69\)		\(101\)	\(36\)	\(65\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(97\)	\(27\)	\(70\)		\(93\)	\(27\)	\(66\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(416\)	\(137\)	\(279\)		\(400\)	\(137\)	\(263\)		\(16\)	\(0\)	\(16\)
Minus space			\(-\)		\(384\)	\(109\)	\(275\)		\(368\)	\(109\)	\(259\)		\(16\)	\(0\)	\(16\)

Trace form

246 * q - 4 * q^2 + 1016 * q^4 - 16 * q^5 - 24 * q^6 - 48 * q^8 + 2214 * q^9 - 12 * q^10 + 96 * q^11 + 12 * q^12 - 26 * q^13 + 144 * q^15 + 3964 * q^16 + 188 * q^17 - 36 * q^18 - 88 * q^19 + 92 * q^20 + 220 * q^22 + 120 * q^23 - 468 * q^24 + 5986 * q^25 - 580 * q^29 - 492 * q^30 - 416 * q^31 - 28 * q^32 - 872 * q^34 + 9144 * q^36 + 52 * q^37 + 2200 * q^38 + 156 * q^39 + 748 * q^40 + 424 * q^41 + 1008 * q^43 + 1044 * q^44 - 144 * q^45 - 360 * q^46 + 1008 * q^47 + 624 * q^48 + 1524 * q^50 - 1032 * q^51 - 780 * q^52 + 140 * q^53 - 216 * q^54 + 2304 * q^55 + 1308 * q^57 + 936 * q^58 + 1072 * q^59 + 828 * q^60 + 1548 * q^61 + 264 * q^62 + 17296 * q^64 + 416 * q^65 - 1764 * q^66 + 2744 * q^67 - 1424 * q^68 + 1416 * q^69 + 1408 * q^71 - 432 * q^72 + 364 * q^73 - 1648 * q^74 - 72 * q^75 - 3032 * q^76 + 156 * q^78 - 1376 * q^79 + 2036 * q^80 + 19926 * q^81 - 932 * q^82 + 4688 * q^83 + 272 * q^85 + 17384 * q^86 + 624 * q^87 + 12156 * q^88 + 896 * q^89 - 108 * q^90 + 11528 * q^92 - 1308 * q^93 - 372 * q^94 + 4584 * q^95 - 1848 * q^96 - 1780 * q^97 + 864 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	13
1911.4.a.a	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				273.4.i.a	$1$	$0$	\(-5\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}-3q^{3}+17q^{4}+3q^{5}+15q^{6}+\cdots\)
1911.4.a.b	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				273.4.i.a	$1$	$1$	\(-5\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}+3q^{3}+17q^{4}-3q^{5}-15q^{6}+\cdots\)
1911.4.a.c	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				273.4.a.a	$1$	$1$	\(-4\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+3q^{3}+8q^{4}-12q^{6}+9q^{9}+\cdots\)
1911.4.a.d	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				273.4.a.c	$1$	$2$	\(-1\)	\(-3\)	\(-9\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-7q^{4}-9q^{5}+3q^{6}+\cdots\)
1911.4.a.e	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				273.4.a.b	$1$	$1$	\(-1\)	\(-3\)	\(5\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
1911.4.a.f	$1911$	$4$	1911.a	1.a	$1$	$1$	$1$	$112.753$	\(\Q\)	None	✓				39.4.a.a	$1$	$0$	\(0\)	\(3\)	\(12\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-8q^{4}+12q^{5}+9q^{9}-6^{2}q^{11}+\cdots\)
1911.4.a.g	$1911$	$4$	1911.a	1.a	$1$	$2$	$2$	$112.753$	\(\Q(\sqrt{865}) \)	None	✓				273.4.a.d	$1$	$1$	\(2\)	\(6\)	\(-5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}+(-3+\beta )q^{5}+\cdots\)
1911.4.a.h	$1911$	$4$	1911.a	1.a	$1$	$2$	$2$	$112.753$	\(\Q(\sqrt{14}) \)	None	✓				39.4.a.b	$1$	$1$	\(2\)	\(6\)	\(-24\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3q^{3}+(7+2\beta )q^{4}+(-12+\cdots)q^{5}+\cdots\)
1911.4.a.i	$1911$	$4$	1911.a	1.a	$1$	$3$	$3$	$112.753$	3.3.4001.1	None	✓				273.4.i.b	$1$	$0$	\(0\)	\(-9\)	\(27\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.j	$1911$	$4$	1911.a	1.a	$1$	$3$	$3$	$112.753$	3.3.4001.1	None	✓				273.4.i.b	$1$	$1$	\(0\)	\(9\)	\(-27\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.k	$1911$	$4$	1911.a	1.a	$1$	$3$	$3$	$112.753$	3.3.3144.1	None	✓				39.4.a.c	$1$	$1$	\(2\)	\(-9\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.l	$1911$	$4$	1911.a	1.a	$1$	$4$	$4$	$112.753$	4.4.1038472.1	None	✓				273.4.a.f	$1$	$0$	\(-3\)	\(-12\)	\(24\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.m	$1911$	$4$	1911.a	1.a	$1$	$4$	$4$	$112.753$	4.4.6295500.1	None	✓				273.4.a.e	$1$	$1$	\(-3\)	\(12\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.n	$1911$	$4$	1911.a	1.a	$1$	$5$	$5$	$112.753$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				273.4.a.g	$1$	$0$	\(5\)	\(15\)	\(-15\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1911.4.a.o	$1911$	$4$	1911.a	1.a	$1$	$6$	$6$	$112.753$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				273.4.a.h	$1$	$0$	\(-6\)	\(18\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.p	$1911$	$4$	1911.a	1.a	$1$	$6$	$6$	$112.753$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				273.4.a.i	$1$	$1$	\(0\)	\(-18\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.q	$1911$	$4$	1911.a	1.a	$1$	$6$	$6$	$112.753$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				273.4.a.j	$1$	$0$	\(7\)	\(-18\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}-3q^{3}+(4+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.r	$1911$	$4$	1911.a	1.a	$1$	$7$	$7$	$112.753$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1911.4.a.r	$1$	$1$	\(-3\)	\(-21\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.4.a.s	$1911$	$4$	1911.a	1.a	$1$	$7$	$7$	$112.753$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1911.4.a.r	$1$	$1$	\(-3\)	\(21\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1911.4.a.t	$1911$	$4$	1911.a	1.a	$1$	$7$	$7$	$112.753$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				273.4.i.c	$1$	$0$	\(8\)	\(-21\)	\(-21\)	\(0\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}-3q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.u	$1911$	$4$	1911.a	1.a	$1$	$7$	$7$	$112.753$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				273.4.i.c	$1$	$1$	\(8\)	\(21\)	\(21\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.v	$1911$	$4$	1911.a	1.a	$1$	$11$	$11$	$112.753$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				273.4.i.d	$1$	$0$	\(-1\)	\(-33\)	\(17\)	\(0\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.4.a.w	$1911$	$4$	1911.a	1.a	$1$	$11$	$11$	$112.753$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		273.4.i.d	$1$	$1$	\(-1\)	\(33\)	\(-17\)	\(0\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.x	$1911$	$4$	1911.a	1.a	$1$	$11$	$11$	$112.753$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓		1911.4.a.x	$1$	$0$	\(1\)	\(-33\)	\(18\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}+(2+\beta _{5}+\cdots)q^{5}+\cdots\)
1911.4.a.y	$1911$	$4$	1911.a	1.a	$1$	$11$	$11$	$112.753$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			1911.4.a.x	$1$	$0$	\(1\)	\(33\)	\(-18\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.z	$1911$	$4$	1911.a	1.a	$1$	$13$	$13$	$112.753$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				273.4.i.f	$1$	$1$	\(-1\)	\(-39\)	\(-39\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots\)
1911.4.a.ba	$1911$	$4$	1911.a	1.a	$1$	$13$	$13$	$112.753$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓		✓		273.4.i.f	$1$	$0$	\(-1\)	\(39\)	\(39\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(3+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.4.a.bb	$1911$	$4$	1911.a	1.a	$1$	$13$	$13$	$112.753$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓		✓		273.4.i.e	$1$	$1$	\(3\)	\(-39\)	\(-15\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1911.4.a.bc	$1911$	$4$	1911.a	1.a	$1$	$13$	$13$	$112.753$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				273.4.i.e	$1$	$0$	\(3\)	\(39\)	\(15\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{8}+\cdots)q^{5}+\cdots\)
1911.4.a.bd	$1911$	$4$	1911.a	1.a	$1$	$14$	$14$	$112.753$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		1911.4.a.bd	$1$	$1$	\(-6\)	\(-42\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
1911.4.a.be	$1911$	$4$	1911.a	1.a	$1$	$14$	$14$	$112.753$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		1911.4.a.bd	$1$	$1$	\(-6\)	\(42\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
1911.4.a.bf	$1911$	$4$	1911.a	1.a	$1$	$22$	$22$	$112.753$		None	✓	✓	✓		1911.4.a.bf	$1$	$0$	\(2\)	\(-66\)	\(-36\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
1911.4.a.bg	$1911$	$4$	1911.a	1.a	$1$	$22$	$22$	$112.753$		None	✓	✓	✓		1911.4.a.bf	$1$	$0$	\(2\)	\(66\)	\(36\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1911))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1911)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)