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	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(1\)
Plus space				\(+\)	\(12\)
Minus space				\(-\)	\(24\)

Trace form

\( 36 q + 36 q^{9} + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(\Gamma_0(2184)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 2}\)