Space of modular forms of level 2184, weight 2, and trivial character

• Label: 2184.2.a
• Level: $2184$
• Weight: $2$
• Character orbit: 2184.a
• Rep. character: $\chi_{2184}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $22$
• Sturm bound: $896$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2184.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(896\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2184))\).

	Total	New	Old
Modular forms	464	36	428
Cusp forms	433	36	397
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(23\)	\(1\)	\(22\)		\(22\)	\(1\)	\(21\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(32\)	\(4\)	\(28\)		\(30\)	\(4\)	\(26\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(32\)	\(4\)	\(28\)		\(30\)	\(4\)	\(26\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(29\)	\(0\)	\(29\)		\(27\)	\(0\)	\(27\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(27\)	\(2\)	\(25\)		\(25\)	\(2\)	\(23\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(30\)	\(2\)	\(28\)		\(28\)	\(2\)	\(26\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(28\)	\(2\)	\(26\)		\(26\)	\(2\)	\(24\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(31\)	\(3\)	\(28\)		\(29\)	\(3\)	\(26\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(35\)	\(2\)	\(33\)		\(33\)	\(2\)	\(31\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(26\)	\(3\)	\(23\)		\(24\)	\(3\)	\(21\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(26\)	\(2\)	\(24\)		\(24\)	\(2\)	\(22\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(29\)	\(2\)	\(27\)		\(27\)	\(2\)	\(25\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(31\)	\(1\)	\(30\)		\(29\)	\(1\)	\(28\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(28\)	\(3\)	\(25\)		\(26\)	\(3\)	\(23\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(30\)	\(4\)	\(26\)		\(28\)	\(4\)	\(24\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(27\)	\(1\)	\(26\)		\(25\)	\(1\)	\(24\)		\(2\)	\(0\)	\(2\)
Plus space				\(+\)		\(220\)	\(12\)	\(208\)		\(205\)	\(12\)	\(193\)		\(15\)	\(0\)	\(15\)
Minus space				\(-\)		\(244\)	\(24\)	\(220\)		\(228\)	\(24\)	\(204\)		\(16\)	\(0\)	\(16\)

Trace form

36 * q + 36 * q^9 + 4 * q^21 + 44 * q^25 + 16 * q^37 + 16 * q^41 + 32 * q^47 + 36 * q^49 + 16 * q^53 + 32 * q^55 + 16 * q^57 + 16 * q^59 + 16 * q^61 - 8 * q^67 + 32 * q^73 + 24 * q^79 + 36 * q^81 - 32 * q^83 + 8 * q^87 + 32 * q^89 - 12 * q^91 + 24 * q^95 + 16 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2184))\) 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	3	7	13
2184.2.a.a	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
2184.2.a.b	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
2184.2.a.c	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
2184.2.a.d	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓	✓	✓	2184.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
2184.2.a.e	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
2184.2.a.f	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
2184.2.a.g	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
2184.2.a.h	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
2184.2.a.i	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.i	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
2184.2.a.j	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓	✓	✓	2184.2.a.j	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
2184.2.a.k	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓	✓	✓	2184.2.a.k	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
2184.2.a.l	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.l	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}-6q^{17}+\cdots\)
2184.2.a.m	$2184$	$2$	2184.a	1.a	$1$	$1$	$1$	$17.439$	\(\Q\)	None	✓	✓			2184.2.a.m	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
2184.2.a.n	$2184$	$2$	2184.a	1.a	$1$	$2$	$2$	$17.439$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		2184.2.a.n	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
2184.2.a.o	$2184$	$2$	2184.a	1.a	$1$	$2$	$2$	$17.439$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	2184.2.a.o	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
2184.2.a.p	$2184$	$2$	2184.a	1.a	$1$	$2$	$2$	$17.439$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	2184.2.a.p	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
2184.2.a.q	$2184$	$2$	2184.a	1.a	$1$	$2$	$2$	$17.439$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	2184.2.a.q	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
2184.2.a.r	$2184$	$2$	2184.a	1.a	$1$	$2$	$2$	$17.439$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓	✓	2184.2.a.r	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
2184.2.a.s	$2184$	$2$	2184.a	1.a	$1$	$3$	$3$	$17.439$	3.3.2089.1	None	✓	✓	✓		2184.2.a.s	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
2184.2.a.t	$2184$	$2$	2184.a	1.a	$1$	$3$	$3$	$17.439$	3.3.961.1	None	✓	✓	✓	✓	2184.2.a.t	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(3-\beta _{1}+\cdots)q^{11}+\cdots\)
2184.2.a.u	$2184$	$2$	2184.a	1.a	$1$	$3$	$3$	$17.439$	3.3.316.1	None	✓	✓	✓	✓	2184.2.a.u	$1$	$0$	\(0\)	\(3\)	\(3\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2184.2.a.v	$2184$	$2$	2184.a	1.a	$1$	$4$	$4$	$17.439$	4.4.138892.1	None	✓	✓	✓	✓	2184.2.a.v	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2184)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 2}\)