Space of modular forms of level 2028, weight 4, and Character 2028.b

• Label: 2028.4.b
• Level: $2028$
• Weight: $4$
• Character orbit: 2028.b
• Rep. character: $\chi_{2028}(337,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $12$
• Sturm bound: $1456$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2028.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1456\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2028, [\chi])\).

	Total	New	Old
Modular forms	1134	78	1056
Cusp forms	1050	78	972
Eisenstein series	84	0	84

Trace form

\( 78 q + 6 q^{3} + 702 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2028.4.b.a	$2028$	$4$	2028.b	13.b	$2$	$2$	$2$	$119.656$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+3iq^{5}-2iq^{7}+9q^{9}+18iq^{11}+\cdots\)
2028.4.b.b	$2028$	$4$	2028.b	13.b	$2$	$2$	$2$	$119.656$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}-2\zeta_{6}q^{5}-11\zeta_{6}q^{7}+9q^{9}+\cdots\)
2028.4.b.c	$2028$	$4$	2028.b	13.b	$2$	$2$	$2$	$119.656$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+9iq^{5}+4iq^{7}+9q^{9}+18iq^{11}+\cdots\)
2028.4.b.d	$2028$	$4$	2028.b	13.b	$2$	$2$	$2$	$119.656$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+iq^{5}-2^{4}iq^{7}+9q^{9}-34iq^{11}+\cdots\)
2028.4.b.e	$2028$	$4$	2028.b	13.b	$2$	$4$	$4$	$119.656$	\(\Q(i, \sqrt{22})\)	None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta _{2}q^{5}+(2\beta _{1}+3\beta _{2})q^{7}+9q^{9}+\cdots\)
2028.4.b.f	$2028$	$4$	2028.b	13.b	$2$	$4$	$4$	$119.656$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+(6\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
2028.4.b.g	$2028$	$4$	2028.b	13.b	$2$	$4$	$4$	$119.656$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+(4\zeta_{12}+3\zeta_{12}^{2})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
2028.4.b.h	$2028$	$4$	2028.b	13.b	$2$	$6$	$6$	$119.656$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-18\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
2028.4.b.i	$2028$	$4$	2028.b	13.b	$2$	$8$	$8$	$119.656$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)	$2^{7}\cdot 3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+9q^{9}-\beta _{4}q^{11}+\cdots\)
2028.4.b.j	$2028$	$4$	2028.b	13.b	$2$	$8$	$8$	$119.656$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(24\)	\(0\)	\(0\)	$2^{7}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta _{6}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+9q^{9}+\cdots\)
2028.4.b.k	$2028$	$4$	2028.b	13.b	$2$	$18$	$18$	$119.656$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(-54\)	\(0\)	\(0\)	$2^{6}\cdot 13^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta _{13}q^{5}-\beta _{15}q^{7}+9q^{9}+\cdots\)
2028.4.b.l	$2028$	$4$	2028.b	13.b	$2$	$18$	$18$	$119.656$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(54\)	\(0\)	\(0\)	$2^{6}\cdot 13^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta _{12}q^{5}+\beta _{14}q^{7}+9q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)