Space of modular forms of level 11900, weight 2, and trivial character

• Label: 11900.2.a
• Level: $11900$
• Weight: $2$
• Character orbit: 11900.a
• Rep. character: $\chi_{11900}(1,\cdot)$
• Character field: $\Q$
• Dimension: $152$
• Newform subspaces: $33$
• Sturm bound: $4320$

Defining parameters

Level:	\( N \)	\(=\)	\( 11900 = 2^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	11900.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 33 \)
Sturm bound:			\(4320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(11900))\).

	Total	New	Old
Modular forms	2196	152	2044
Cusp forms	2125	152	1973
Eisenstein series	71	0	71

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

\(2\)	\(5\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(120\)	\(0\)	\(120\)		\(115\)	\(0\)	\(115\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(156\)	\(0\)	\(156\)		\(150\)	\(0\)	\(150\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(150\)	\(0\)	\(150\)		\(144\)	\(0\)	\(144\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(126\)	\(0\)	\(126\)		\(120\)	\(0\)	\(120\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(146\)	\(0\)	\(146\)		\(140\)	\(0\)	\(140\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(130\)	\(0\)	\(130\)		\(124\)	\(0\)	\(124\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(136\)	\(0\)	\(136\)		\(130\)	\(0\)	\(130\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(140\)	\(0\)	\(140\)		\(134\)	\(0\)	\(134\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(132\)	\(18\)	\(114\)		\(129\)	\(18\)	\(111\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(141\)	\(18\)	\(123\)		\(138\)	\(18\)	\(120\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(147\)	\(18\)	\(129\)		\(144\)	\(18\)	\(126\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(126\)	\(18\)	\(108\)		\(123\)	\(18\)	\(105\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(136\)	\(20\)	\(116\)		\(133\)	\(20\)	\(113\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(137\)	\(20\)	\(117\)		\(134\)	\(20\)	\(114\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(131\)	\(20\)	\(111\)		\(128\)	\(20\)	\(108\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(142\)	\(20\)	\(122\)		\(139\)	\(20\)	\(119\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(1078\)	\(76\)	\(1002\)		\(1043\)	\(76\)	\(967\)		\(35\)	\(0\)	\(35\)
Minus space				\(-\)		\(1118\)	\(76\)	\(1042\)		\(1082\)	\(76\)	\(1006\)		\(36\)	\(0\)	\(36\)

Trace form

152 * q + 4 * q^3 + 156 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^19 + 8 * q^23 - 8 * q^27 - 20 * q^29 + 20 * q^31 - 28 * q^33 + 16 * q^37 - 20 * q^39 + 4 * q^41 + 4 * q^43 - 32 * q^47 + 152 * q^49 - 4 * q^51 + 12 * q^53 - 12 * q^57 + 32 * q^59 + 20 * q^61 - 8 * q^63 + 4 * q^67 - 116 * q^69 - 64 * q^71 + 28 * q^73 + 20 * q^79 + 56 * q^81 - 44 * q^83 - 28 * q^87 - 72 * q^89 - 4 * q^91 - 24 * q^93 + 20 * q^97 - 128 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(11900))\) 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	7	17
11900.2.a.a	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
11900.2.a.b	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+7q^{13}+q^{17}+4q^{19}+\cdots\)
11900.2.a.c	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+5q^{11}+2q^{13}+q^{17}+\cdots\)
11900.2.a.d	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+6q^{11}-2q^{13}+q^{17}+\cdots\)
11900.2.a.e	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}-7q^{13}-q^{17}+4q^{19}+\cdots\)
11900.2.a.f	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+5q^{11}-2q^{13}-q^{17}+\cdots\)
11900.2.a.g	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+6q^{11}+2q^{13}-q^{17}+\cdots\)
11900.2.a.h	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
11900.2.a.i	$11900$	$2$	11900.a	1.a	$1$	$1$	$1$	$95.022$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
11900.2.a.j	$11900$	$2$	11900.a	1.a	$1$	$2$	$2$	$95.022$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.k	$11900$	$2$	11900.a	1.a	$1$	$2$	$2$	$95.022$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
11900.2.a.l	$11900$	$2$	11900.a	1.a	$1$	$2$	$2$	$95.022$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.m	$11900$	$2$	11900.a	1.a	$1$	$2$	$2$	$95.022$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.n	$11900$	$2$	11900.a	1.a	$1$	$3$	$3$	$95.022$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.o	$11900$	$2$	11900.a	1.a	$1$	$3$	$3$	$95.022$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(0\)	\(4\)	\(0\)	\(-3\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.p	$11900$	$2$	11900.a	1.a	$1$	$4$	$4$	$95.022$	4.4.32081.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.q	$11900$	$2$	11900.a	1.a	$1$	$4$	$4$	$95.022$	4.4.16609.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
11900.2.a.r	$11900$	$2$	11900.a	1.a	$1$	$4$	$4$	$95.022$	4.4.53121.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.s	$11900$	$2$	11900.a	1.a	$1$	$4$	$4$	$95.022$	4.4.35537.3	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.t	$11900$	$2$	11900.a	1.a	$1$	$4$	$4$	$95.022$	4.4.30273.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
11900.2.a.u	$11900$	$2$	11900.a	1.a	$1$	$5$	$5$	$95.022$	5.5.11858473.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-5\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.v	$11900$	$2$	11900.a	1.a	$1$	$7$	$7$	$95.022$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-4\)	\(0\)	\(-7\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.w	$11900$	$2$	11900.a	1.a	$1$	$7$	$7$	$95.022$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-2\)	\(0\)	\(7\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
11900.2.a.x	$11900$	$2$	11900.a	1.a	$1$	$7$	$7$	$95.022$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-7\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.y	$11900$	$2$	11900.a	1.a	$1$	$7$	$7$	$95.022$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(0\)	\(7\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.z	$11900$	$2$	11900.a	1.a	$1$	$8$	$8$	$95.022$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-8\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
11900.2.a.ba	$11900$	$2$	11900.a	1.a	$1$	$8$	$8$	$95.022$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.bb	$11900$	$2$	11900.a	1.a	$1$	$8$	$8$	$95.022$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(2\)	\(0\)	\(-8\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.bc	$11900$	$2$	11900.a	1.a	$1$	$8$	$8$	$95.022$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(2\)	\(0\)	\(8\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.bd	$11900$	$2$	11900.a	1.a	$1$	$10$	$10$	$95.022$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-2\)	\(0\)	\(-10\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
11900.2.a.be	$11900$	$2$	11900.a	1.a	$1$	$10$	$10$	$95.022$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(2\)	\(0\)	\(10\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
11900.2.a.bf	$11900$	$2$	11900.a	1.a	$1$	$12$	$12$	$95.022$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-2\)	\(0\)	\(12\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
11900.2.a.bg	$11900$	$2$	11900.a	1.a	$1$	$12$	$12$	$95.022$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(2\)	\(0\)	\(-12\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(11900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(11900)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(595))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2975))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5950))\)\(^{\oplus 2}\)