Space of modular forms of level 2340, weight 2, and trivial character

• Label: 2340.2.a
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.a
• Rep. character: $\chi_{2340}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $14$
• Sturm bound: $1008$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1008\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2340))\).

	Total	New	Old
Modular forms	528	20	508
Cusp forms	481	20	461
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(5\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(31\)	\(0\)	\(31\)		\(28\)	\(0\)	\(28\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(35\)	\(0\)	\(35\)		\(31\)	\(0\)	\(31\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(35\)	\(0\)	\(35\)		\(31\)	\(0\)	\(31\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(31\)	\(0\)	\(31\)		\(27\)	\(0\)	\(27\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(34\)	\(0\)	\(34\)		\(30\)	\(0\)	\(30\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(34\)	\(0\)	\(34\)		\(30\)	\(0\)	\(30\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(34\)	\(0\)	\(34\)		\(30\)	\(0\)	\(30\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(34\)	\(0\)	\(34\)		\(30\)	\(0\)	\(30\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(35\)	\(1\)	\(34\)		\(33\)	\(1\)	\(32\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(31\)	\(3\)	\(28\)		\(29\)	\(3\)	\(26\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(31\)	\(1\)	\(30\)		\(29\)	\(1\)	\(28\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(35\)	\(3\)	\(32\)		\(33\)	\(3\)	\(30\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(32\)	\(3\)	\(29\)		\(30\)	\(3\)	\(27\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(32\)	\(4\)	\(28\)		\(30\)	\(4\)	\(26\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(32\)	\(4\)	\(28\)		\(30\)	\(4\)	\(26\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(32\)	\(1\)	\(31\)		\(30\)	\(1\)	\(29\)		\(2\)	\(0\)	\(2\)
Plus space				\(+\)		\(256\)	\(8\)	\(248\)		\(233\)	\(8\)	\(225\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(272\)	\(12\)	\(260\)		\(248\)	\(12\)	\(236\)		\(24\)	\(0\)	\(24\)

Trace form

20 * q - 2 * q^5 - 4 * q^11 + 2 * q^13 - 4 * q^17 + 8 * q^19 + 8 * q^23 + 20 * q^25 - 8 * q^29 + 4 * q^31 - 4 * q^35 - 8 * q^37 + 4 * q^41 + 16 * q^43 - 16 * q^47 + 12 * q^49 + 16 * q^53 + 4 * q^55 + 8 * q^59 + 8 * q^61 - 4 * q^65 + 24 * q^67 + 24 * q^71 + 24 * q^73 + 36 * q^77 - 8 * q^89 + 4 * q^91 + 8 * q^95 - 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2340))\) 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	5	13
2340.2.a.a	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓				780.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+2q^{11}-q^{13}+2q^{17}+\cdots\)
2340.2.a.b	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓	✓	✓	✓	2340.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+q^{11}-q^{13}+5q^{17}+\cdots\)
2340.2.a.c	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓	✓			2340.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-6q^{11}+q^{13}+4q^{17}+4q^{19}+\cdots\)
2340.2.a.d	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓				780.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-q^{11}+q^{13}+3q^{17}+\cdots\)
2340.2.a.e	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓				780.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+6q^{11}-q^{13}+2q^{17}+\cdots\)
2340.2.a.f	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓		✓	✓	780.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
2340.2.a.g	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓	✓	✓	✓	2340.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-q^{11}-q^{13}-5q^{17}+\cdots\)
2340.2.a.h	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓	✓			2340.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+6q^{11}+q^{13}-4q^{17}+4q^{19}+\cdots\)
2340.2.a.i	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	\(\Q\)	None	✓				260.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
2340.2.a.j	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓		2340.2.a.j	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+(2-\beta )q^{11}+q^{13}+(-4+\cdots)q^{17}+\cdots\)
2340.2.a.k	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	\(\Q(\sqrt{17}) \)	None	✓		✓		780.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}-q^{13}+\cdots\)
2340.2.a.l	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	\(\Q(\sqrt{73}) \)	None	✓		✓		780.2.a.e	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}-\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
2340.2.a.m	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓		2340.2.a.j	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+(-2+\beta )q^{11}+q^{13}+\cdots\)
2340.2.a.n	$2340$	$2$	2340.a	1.a	$1$	$3$	$3$	$18.685$	3.3.564.1	None	✓		✓		260.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta _{1})q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2340))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2340)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1170))\)\(^{\oplus 2}\)