Space of modular forms of level 2300, weight 2, and trivial character

• Label: 2300.2.a
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.a
• Rep. character: $\chi_{2300}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $15$
• Sturm bound: $720$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(720\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2300))\).

	Total	New	Old
Modular forms	378	36	342
Cusp forms	343	36	307
Eisenstein series	35	0	35

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

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(39\)	\(0\)	\(39\)		\(34\)	\(0\)	\(34\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(57\)	\(0\)	\(57\)		\(51\)	\(0\)	\(51\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(57\)	\(0\)	\(57\)		\(51\)	\(0\)	\(51\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(39\)	\(0\)	\(39\)		\(33\)	\(0\)	\(33\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(42\)	\(8\)	\(34\)		\(39\)	\(8\)	\(31\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(51\)	\(8\)	\(43\)		\(48\)	\(8\)	\(40\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(51\)	\(10\)	\(41\)		\(48\)	\(10\)	\(38\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(42\)	\(10\)	\(32\)		\(39\)	\(10\)	\(29\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(180\)	\(18\)	\(162\)		\(163\)	\(18\)	\(145\)		\(17\)	\(0\)	\(17\)
Minus space			\(-\)		\(198\)	\(18\)	\(180\)		\(180\)	\(18\)	\(162\)		\(18\)	\(0\)	\(18\)

Trace form

36 * q - 2 * q^3 + 6 * q^7 + 34 * q^9 - 6 * q^11 + 6 * q^13 - 10 * q^17 + 4 * q^19 - 2 * q^21 - 2 * q^27 - 18 * q^29 + 10 * q^31 + 6 * q^33 + 10 * q^37 + 6 * q^39 - 14 * q^41 - 6 * q^47 + 56 * q^49 - 18 * q^51 - 4 * q^53 - 8 * q^57 - 28 * q^59 + 8 * q^63 - 10 * q^67 + 4 * q^69 - 10 * q^71 + 14 * q^73 - 20 * q^77 + 12 * q^81 - 10 * q^83 - 22 * q^87 - 12 * q^89 - 22 * q^91 + 6 * q^93 + 18 * q^97 - 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\) 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	23
2300.2.a.a	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				460.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
2300.2.a.b	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓	✓			2300.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
2300.2.a.c	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
2300.2.a.d	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				460.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}-2q^{9}-6q^{11}+q^{13}+\cdots\)
2300.2.a.e	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				460.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+6q^{11}-6q^{13}-7q^{17}+\cdots\)
2300.2.a.f	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				460.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}-2q^{9}-4q^{11}-q^{13}+\cdots\)
2300.2.a.g	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓	✓			2300.2.a.b	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
2300.2.a.h	$2300$	$2$	2300.a	1.a	$1$	$1$	$1$	$18.366$	\(\Q\)	None	✓				92.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{7}+6q^{9}+2q^{11}+5q^{13}+\cdots\)
2300.2.a.i	$2300$	$2$	2300.a	1.a	$1$	$2$	$2$	$18.366$	\(\Q(\sqrt{17}) \)	None	✓				460.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
2300.2.a.j	$2300$	$2$	2300.a	1.a	$1$	$3$	$3$	$18.366$	3.3.321.1	None	✓	✓	✓		2300.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2300.2.a.k	$2300$	$2$	2300.a	1.a	$1$	$3$	$3$	$18.366$	3.3.321.1	None	✓	✓			2300.2.a.j	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
2300.2.a.l	$2300$	$2$	2300.a	1.a	$1$	$4$	$4$	$18.366$	4.4.53121.1	None	✓	✓			2300.2.a.l	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.a.m	$2300$	$2$	2300.a	1.a	$1$	$4$	$4$	$18.366$	4.4.53121.1	None	✓	✓	✓		2300.2.a.l	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2300.2.a.n	$2300$	$2$	2300.a	1.a	$1$	$6$	$6$	$18.366$	6.6.143376304.1	None	✓		✓		460.2.c.a	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(-9\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
2300.2.a.o	$2300$	$2$	2300.a	1.a	$1$	$6$	$6$	$18.366$	6.6.143376304.1	None	✓		✓		460.2.c.a	$1$	$0$	\(0\)	\(4\)	\(0\)	\(9\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2300)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 2}\)