Space of modular forms of level 2028, weight 2, and Character 2028.i

• Label: 2028.2.i
• Level: $2028$
• Weight: $2$
• Character orbit: 2028.i
• Rep. character: $\chi_{2028}(529,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $14$
• Sturm bound: $728$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(728\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2028, [\chi])\).

	Total	New	Old
Modular forms	812	54	758
Cusp forms	644	54	590
Eisenstein series	168	0	168

Trace form

54 * q - q^3 - 4 * q^5 + q^7 - 27 * q^9 + 2 * q^11 - 2 * q^15 - 8 * q^17 + 4 * q^19 + 2 * q^21 + 10 * q^23 + 50 * q^25 + 2 * q^27 + 6 * q^29 + 2 * q^31 - 2 * q^33 + 6 * q^35 + 10 * q^37 - 4 * q^41 + 5 * q^43 + 2 * q^45 + 20 * q^47 - 34 * q^49 - 16 * q^51 - 16 * q^53 + 8 * q^55 + 8 * q^57 - 2 * q^59 - 5 * q^61 + q^63 - 7 * q^67 - 2 * q^69 + 10 * q^71 + 14 * q^73 + q^75 + 12 * q^77 - 42 * q^79 - 27 * q^81 - 24 * q^83 - 8 * q^85 - 10 * q^87 - 16 * q^89 + q^93 + 4 * q^95 + 13 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2028, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2028.2.i.a	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.b.b	$2$	$1$	\(0\)	\(-1\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.b	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.c	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.d	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.b.b	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.e	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.a.a	$2$	$1$	\(0\)	\(1\)	\(-8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-4q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.f	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.i.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.g	$2028$	$2$	2028.i	13.c	$3$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.a.a	$2$	$0$	\(0\)	\(1\)	\(8\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
2028.2.i.h	$2028$	$2$	2028.i	13.c	$3$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.q.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{3}-\beta_{3} q^{5}+(-2\beta_{3}+2\beta_{2})q^{7}+\cdots\)
2028.2.i.i	$2028$	$2$	2028.i	13.c	$3$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.b.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta_1 q^{3}-\beta_{3} q^{5}+(\beta_1-1)q^{9}+\cdots\)
2028.2.i.j	$2028$	$2$	2028.i	13.c	$3$	$6$	$3$	$16.194$	6.0.64827.1	None		✓			2028.2.a.k	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{5})q^{3}+(1-2\beta _{2}+\beta _{3})q^{5}+\cdots\)
2028.2.i.k	$2028$	$2$	2028.i	13.c	$3$	$6$	$3$	$16.194$	6.0.64827.1	None		✓			2028.2.a.k	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(-1+2\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
2028.2.i.l	$2028$	$2$	2028.i	13.c	$3$	$6$	$3$	$16.194$	6.0.64827.1	None		✓			2028.2.a.i	$2$	$0$	\(0\)	\(3\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2028.2.i.m	$2028$	$2$	2028.i	13.c	$3$	$6$	$3$	$16.194$	6.0.64827.1	None		✓			2028.2.a.i	$2$	$0$	\(0\)	\(3\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{1}+2\beta _{4}+\cdots)q^{7}+\cdots\)
2028.2.i.n	$2028$	$2$	2028.i	13.c	$3$	$8$	$4$	$16.194$	8.0.\(\cdots\).2	None			✓		156.2.q.b	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{3}+(-\beta _{4}+\beta _{5}-\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)