Space of modular forms of level 19275, weight 2, and trivial character

• Label: 19275.2.a
• Level: $19275$
• Weight: $2$
• Character orbit: 19275.a
• Rep. character: $\chi_{19275}(1,\cdot)$
• Character field: $\Q$
• Dimension: $810$
• Newform subspaces: $28$
• Sturm bound: $5160$

Defining parameters

Level:	\( N \)	\(=\)	\( 19275 = 3 \cdot 5^{2} \cdot 257 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19275.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(5160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(19275))\).

	Total	New	Old
Modular forms	2592	810	1782
Cusp forms	2569	810	1759
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.

\(3\)	\(5\)	\(257\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(303\)	\(94\)	\(209\)		\(301\)	\(94\)	\(207\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(345\)	\(100\)	\(245\)		\(342\)	\(100\)	\(242\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(339\)	\(112\)	\(227\)		\(336\)	\(112\)	\(224\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(309\)	\(100\)	\(209\)		\(306\)	\(100\)	\(206\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(321\)	\(98\)	\(223\)		\(318\)	\(98\)	\(220\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(327\)	\(92\)	\(235\)		\(324\)	\(92\)	\(232\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(333\)	\(101\)	\(232\)		\(330\)	\(101\)	\(229\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(315\)	\(113\)	\(202\)		\(312\)	\(113\)	\(199\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(1272\)	\(387\)	\(885\)		\(1261\)	\(387\)	\(874\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(1320\)	\(423\)	\(897\)		\(1308\)	\(423\)	\(885\)		\(12\)	\(0\)	\(12\)

Trace form

810 * q - 4 * q^2 - 2 * q^3 + 804 * q^4 + 2 * q^6 - 12 * q^8 + 810 * q^9 + 2 * q^12 - 8 * q^13 + 20 * q^14 + 816 * q^16 - 4 * q^18 + 8 * q^19 - 16 * q^21 - 8 * q^22 + 12 * q^23 - 6 * q^24 + 4 * q^26 - 2 * q^27 - 28 * q^28 - 4 * q^31 - 68 * q^32 + 12 * q^33 - 24 * q^34 + 804 * q^36 - 40 * q^37 - 20 * q^38 - 8 * q^39 + 16 * q^41 - 16 * q^42 + 4 * q^43 - 24 * q^44 - 92 * q^46 - 16 * q^47 - 14 * q^48 + 822 * q^49 + 8 * q^51 - 60 * q^52 - 24 * q^53 + 2 * q^54 - 8 * q^56 - 12 * q^57 + 32 * q^59 - 8 * q^61 - 52 * q^62 + 732 * q^64 + 16 * q^67 + 28 * q^68 + 28 * q^71 - 12 * q^72 + 4 * q^73 - 16 * q^74 + 32 * q^76 + 28 * q^77 - 64 * q^79 + 810 * q^81 - 44 * q^82 + 4 * q^83 - 52 * q^84 - 44 * q^86 + 8 * q^87 - 32 * q^88 + 52 * q^89 - 4 * q^91 - 56 * q^92 - 24 * q^93 + 60 * q^94 - 10 * q^96 - 12 * q^97 - 44 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(19275))\) 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	5	257
19275.2.a.a	$19275$	$2$	19275.a	1.a	$1$	$1$	$1$	$153.912$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
19275.2.a.b	$19275$	$2$	19275.a	1.a	$1$	$1$	$1$	$153.912$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
19275.2.a.c	$19275$	$2$	19275.a	1.a	$1$	$2$	$2$	$153.912$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.d	$19275$	$2$	19275.a	1.a	$1$	$6$	$6$	$153.912$	6.6.1292517.1	None	✓	?				$-1$		\(6\)	\(-6\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.e	$19275$	$2$	19275.a	1.a	$1$	$8$	$8$	$153.912$	8.8.6293053097.1	None	✓	?				$-1$		\(-1\)	\(8\)	\(0\)	\(6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.f	$19275$	$2$	19275.a	1.a	$1$	$8$	$8$	$153.912$	8.8.2318650669.1	None	✓	?				$-1$		\(3\)	\(8\)	\(0\)	\(-12\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.g	$19275$	$2$	19275.a	1.a	$1$	$9$	$9$	$153.912$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(9\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.h	$19275$	$2$	19275.a	1.a	$1$	$13$	$13$	$153.912$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(-5\)	\(-13\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
19275.2.a.i	$19275$	$2$	19275.a	1.a	$1$	$14$	$14$	$153.912$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(14\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.j	$19275$	$2$	19275.a	1.a	$1$	$15$	$15$	$153.912$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(-15\)	\(0\)	\(10\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.k	$19275$	$2$	19275.a	1.a	$1$	$15$	$15$	$153.912$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(-15\)	\(0\)	\(14\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
19275.2.a.l	$19275$	$2$	19275.a	1.a	$1$	$17$	$17$	$153.912$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(17\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.m	$19275$	$2$	19275.a	1.a	$1$	$25$	$25$	$153.912$		None	✓	?				$-1$		\(-10\)	\(25\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.n	$19275$	$2$	19275.a	1.a	$1$	$25$	$25$	$153.912$		None	✓	?				$-1$		\(-4\)	\(25\)	\(0\)	\(10\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.o	$19275$	$2$	19275.a	1.a	$1$	$28$	$28$	$153.912$		None	✓	?				$-1$		\(-7\)	\(-28\)	\(0\)	\(-20\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.p	$19275$	$2$	19275.a	1.a	$1$	$29$	$29$	$153.912$		None	✓	?				$-1$		\(-4\)	\(-29\)	\(0\)	\(-12\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
19275.2.a.q	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?				$-1$		\(-6\)	\(-42\)	\(0\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.r	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?	✓			$-1$		\(-4\)	\(42\)	\(0\)	\(-13\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.s	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?				$-1$		\(-4\)	\(42\)	\(0\)	\(-9\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.t	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?	✓			$-1$		\(4\)	\(-42\)	\(0\)	\(9\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
19275.2.a.u	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?				$-1$		\(4\)	\(-42\)	\(0\)	\(13\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.v	$19275$	$2$	19275.a	1.a	$1$	$42$	$42$	$153.912$		None	✓	?	✓			$-1$		\(6\)	\(42\)	\(0\)	\(7\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.w	$19275$	$2$	19275.a	1.a	$1$	$43$	$43$	$153.912$		None	✓	?	✓			$-1$		\(-4\)	\(-43\)	\(0\)	\(-10\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.x	$19275$	$2$	19275.a	1.a	$1$	$43$	$43$	$153.912$		None	✓	?				$-1$		\(4\)	\(43\)	\(0\)	\(10\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
19275.2.a.y	$19275$	$2$	19275.a	1.a	$1$	$58$	$58$	$153.912$		None	✓	?	✓			$-1$		\(-7\)	\(58\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
19275.2.a.z	$19275$	$2$	19275.a	1.a	$1$	$58$	$58$	$153.912$		None	✓	?	✓			$-1$		\(7\)	\(-58\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
19275.2.a.ba	$19275$	$2$	19275.a	1.a	$1$	$70$	$70$	$153.912$		None	✓	?	✓			$-1$		\(-9\)	\(-70\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
19275.2.a.bb	$19275$	$2$	19275.a	1.a	$1$	$70$	$70$	$153.912$		None	✓	?	✓			$-1$		\(9\)	\(70\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(19275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(19275)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(257))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(771))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6425))\)\(^{\oplus 2}\)