Space of modular forms of level 2128, weight 2, and trivial character

• Label: 2128.2.a
• Level: $2128$
• Weight: $2$
• Character orbit: 2128.a
• Rep. character: $\chi_{2128}(1,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $22$
• Sturm bound: $640$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2128 = 2^{4} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2128.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(640\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2128))\).

	Total	New	Old
Modular forms	332	54	278
Cusp forms	309	54	255
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.

\(2\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(39\)	\(6\)	\(33\)		\(37\)	\(6\)	\(31\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(44\)	\(7\)	\(37\)		\(41\)	\(7\)	\(34\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(41\)	\(7\)	\(34\)		\(38\)	\(7\)	\(31\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(42\)	\(6\)	\(36\)		\(39\)	\(6\)	\(33\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(44\)	\(7\)	\(37\)		\(41\)	\(7\)	\(34\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(39\)	\(6\)	\(33\)		\(36\)	\(6\)	\(30\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(42\)	\(7\)	\(35\)		\(39\)	\(7\)	\(32\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(41\)	\(8\)	\(33\)		\(38\)	\(8\)	\(30\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(162\)	\(25\)	\(137\)		\(151\)	\(25\)	\(126\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(170\)	\(29\)	\(141\)		\(158\)	\(29\)	\(129\)		\(12\)	\(0\)	\(12\)

Trace form

54 * q + 4 * q^5 + 2 * q^7 + 54 * q^9 - 8 * q^11 + 4 * q^13 - 24 * q^15 - 4 * q^17 + 16 * q^23 + 50 * q^25 - 4 * q^29 - 12 * q^35 + 12 * q^37 + 16 * q^39 - 4 * q^41 + 24 * q^43 + 20 * q^45 - 48 * q^47 + 54 * q^49 - 24 * q^51 - 4 * q^53 + 32 * q^55 + 20 * q^61 + 10 * q^63 - 24 * q^65 + 20 * q^67 - 20 * q^71 - 20 * q^73 + 8 * q^75 - 8 * q^77 - 4 * q^79 + 54 * q^81 + 24 * q^85 + 24 * q^87 - 20 * q^89 - 48 * q^93 + 16 * q^95 - 4 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\) 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	7	19
2128.2.a.a	$2128$	$2$	2128.a	1.a	$1$	$1$	$1$	$16.992$	\(\Q\)	None	✓				532.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
2128.2.a.b	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				266.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-3\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.c	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				133.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
2128.2.a.d	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.e	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				532.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
2128.2.a.f	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
2128.2.a.g	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{29}) \)	None	✓				266.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(4+\beta )q^{9}+\cdots\)
2128.2.a.h	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{13}) \)	None	✓				266.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
2128.2.a.i	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{13}) \)	None	✓				1064.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+q^{7}+\beta q^{9}+(1-\beta )q^{11}+\cdots\)
2128.2.a.j	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+2\beta )q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
2128.2.a.k	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{21}) \)	None	✓				532.2.a.c	$1$	$0$	\(0\)	\(1\)	\(6\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+3q^{5}-q^{7}+(2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
2128.2.a.l	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{13}) \)	None	✓				133.2.a.b	$1$	$0$	\(0\)	\(3\)	\(-6\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-3q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
2128.2.a.m	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				532.2.a.b	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
2128.2.a.n	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.a	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(1-2\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.o	$2128$	$2$	2128.a	1.a	$1$	$2$	$2$	$16.992$	\(\Q(\sqrt{5}) \)	None	✓				133.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
2128.2.a.p	$2128$	$2$	2128.a	1.a	$1$	$3$	$3$	$16.992$	3.3.229.1	None	✓		✓		133.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2128.2.a.q	$2128$	$2$	2128.a	1.a	$1$	$3$	$3$	$16.992$	3.3.1101.1	None	✓		✓		1064.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
2128.2.a.r	$2128$	$2$	2128.a	1.a	$1$	$3$	$3$	$16.992$	3.3.733.1	None	✓				532.2.a.e	$1$	$0$	\(0\)	\(1\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
2128.2.a.s	$2128$	$2$	2128.a	1.a	$1$	$3$	$3$	$16.992$	3.3.469.1	None	✓				266.2.a.d	$1$	$0$	\(0\)	\(1\)	\(5\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2128.2.a.t	$2128$	$2$	2128.a	1.a	$1$	$4$	$4$	$16.992$	4.4.25857.1	None	✓		✓		1064.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
2128.2.a.u	$2128$	$2$	2128.a	1.a	$1$	$4$	$4$	$16.992$	4.4.18097.1	None	✓		✓		1064.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
2128.2.a.v	$2128$	$2$	2128.a	1.a	$1$	$5$	$5$	$16.992$	5.5.10463409.1	None	✓		✓		1064.2.a.i	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2128)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 2}\)