Space of modular forms of level 6128, weight 2, and trivial character

• Label: 6128.2.a
• Level: $6128$
• Weight: $2$
• Character orbit: 6128.a
• Rep. character: $\chi_{6128}(1,\cdot)$
• Character field: $\Q$
• Dimension: $191$
• Newform subspaces: $18$
• Sturm bound: $1536$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6128 = 2^{4} \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6128.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1536\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6128))\).

	Total	New	Old
Modular forms	774	191	583
Cusp forms	763	191	572
Eisenstein series	11	0	11

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

\(2\)	\(383\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(48\)
\(+\)	\(-\)	\(-\)	\(48\)
\(-\)	\(+\)	\(-\)	\(56\)
\(-\)	\(-\)	\(+\)	\(39\)
Plus space		\(+\)	\(87\)
Minus space		\(-\)	\(104\)

Trace form

191 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 187 * q^9 - 4 * q^11 - 2 * q^13 - 2 * q^17 + 10 * q^19 + 2 * q^23 + 185 * q^25 - 4 * q^27 + 6 * q^29 + 10 * q^31 - 8 * q^33 - 2 * q^37 - 8 * q^39 + 6 * q^41 + 18 * q^43 - 10 * q^45 + 191 * q^49 + 12 * q^51 + 6 * q^53 + 28 * q^55 - 8 * q^57 - 16 * q^59 - 10 * q^61 + 6 * q^63 - 4 * q^65 + 2 * q^67 - 16 * q^69 - 22 * q^71 - 2 * q^73 - 14 * q^75 - 8 * q^77 + 20 * q^79 + 167 * q^81 + 24 * q^83 - 28 * q^85 - 28 * q^87 + 6 * q^89 + 4 * q^91 - 8 * q^93 - 12 * q^95 + 6 * q^97 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6128))\) 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	383
6128.2.a.a	$6128$	$2$	6128.a	1.a	$1$	$1$	$1$	$48.932$	\(\Q\)	None	✓				766.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
6128.2.a.b	$6128$	$2$	6128.a	1.a	$1$	$2$	$2$	$48.932$	\(\Q(\sqrt{21}) \)	None	✓				3064.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-2+\beta )q^{5}+3q^{7}+(2+\beta )q^{9}+\cdots\)
6128.2.a.c	$6128$	$2$	6128.a	1.a	$1$	$2$	$2$	$48.932$	\(\Q(\sqrt{5}) \)	None	✓				383.2.a.a	$1$	$1$	\(0\)	\(3\)	\(1\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(3-2\beta )q^{7}+\cdots\)
6128.2.a.d	$6128$	$2$	6128.a	1.a	$1$	$3$	$3$	$48.932$	3.3.469.1	None	✓				3064.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
6128.2.a.e	$6128$	$2$	6128.a	1.a	$1$	$4$	$4$	$48.932$	4.4.15952.1	None	✓				766.2.a.b	$1$	$1$	\(0\)	\(-8\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
6128.2.a.f	$6128$	$2$	6128.a	1.a	$1$	$4$	$4$	$48.932$	4.4.11661.1	None	✓				1532.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots\)
6128.2.a.g	$6128$	$2$	6128.a	1.a	$1$	$5$	$5$	$48.932$	5.5.89417.1	None	✓				766.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
6128.2.a.h	$6128$	$2$	6128.a	1.a	$1$	$5$	$5$	$48.932$	\(\Q(\zeta_{22})^+\)	None	✓				766.2.a.d	$1$	$0$	\(0\)	\(4\)	\(-5\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{4})q^{5}+\cdots\)
6128.2.a.i	$6128$	$2$	6128.a	1.a	$1$	$6$	$6$	$48.932$	6.6.3151861.1	None	✓				383.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(1+\beta _{5})q^{7}+\cdots\)
6128.2.a.j	$6128$	$2$	6128.a	1.a	$1$	$6$	$6$	$48.932$	6.6.26017969.1	None	✓				766.2.a.e	$1$	$1$	\(0\)	\(4\)	\(1\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(\beta _{4}+\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots\)
6128.2.a.k	$6128$	$2$	6128.a	1.a	$1$	$10$	$10$	$48.932$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				766.2.a.f	$1$	$0$	\(0\)	\(0\)	\(3\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{5}q^{5}+(1-\beta _{2}-\beta _{3})q^{7}+\cdots\)
6128.2.a.l	$6128$	$2$	6128.a	1.a	$1$	$12$	$12$	$48.932$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		1532.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-23\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+(-2+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
6128.2.a.m	$6128$	$2$	6128.a	1.a	$1$	$16$	$16$	$48.932$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				1532.2.a.c	$1$	$0$	\(0\)	\(5\)	\(-3\)	\(18\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{9}q^{5}+(1+\beta _{11})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
6128.2.a.n	$6128$	$2$	6128.a	1.a	$1$	$19$	$19$	$48.932$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓				3064.2.a.c	$1$	$1$	\(0\)	\(4\)	\(-7\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}+\beta _{10})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
6128.2.a.o	$6128$	$2$	6128.a	1.a	$1$	$21$	$21$	$48.932$		None	✓				3064.2.a.d	$1$	$0$	\(0\)	\(5\)	\(-2\)	\(11\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6128.2.a.p	$6128$	$2$	6128.a	1.a	$1$	$24$	$24$	$48.932$		None	✓		✓		383.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-17\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6128.2.a.q	$6128$	$2$	6128.a	1.a	$1$	$24$	$24$	$48.932$		None	✓		✓		3064.2.a.e	$1$	$0$	\(0\)	\(0\)	\(11\)	\(5\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6128.2.a.r	$6128$	$2$	6128.a	1.a	$1$	$27$	$27$	$48.932$		None	✓		✓		3064.2.a.f	$1$	$1$	\(0\)	\(-7\)	\(0\)	\(-13\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6128)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(383))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(766))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1532))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3064))\)\(^{\oplus 2}\)