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

• Label: 2028.2.q
• Level: $2028$
• Weight: $2$
• Character orbit: 2028.q
• Rep. character: $\chi_{2028}(361,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $50$
• Newform subspaces: $10$
• 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.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(728\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	812	50	762
Cusp forms	644	50	594
Eisenstein series	168	0	168

Trace form

50 * q + q^3 - 3 * q^7 - 25 * q^9 - 18 * q^11 - 6 * q^15 + 6 * q^17 + 18 * q^19 - 2 * q^23 - 26 * q^25 - 2 * q^27 + 4 * q^29 + 6 * q^33 + 18 * q^35 - 6 * q^37 + 6 * q^41 - 15 * q^43 + 14 * q^49 + 16 * q^51 + 36 * q^53 + 4 * q^55 - 6 * q^59 - q^61 + 3 * q^63 - 21 * q^67 - 14 * q^69 - 6 * q^71 - 15 * q^75 - 28 * q^77 - 22 * q^79 - 25 * q^81 + 54 * q^85 - 18 * q^87 - 12 * q^89 - 15 * q^93 + 4 * q^95 - 39 * q^97

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.q.a	$2028$	$2$	2028.q	13.e	$6$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.q.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(1-2\zeta_{6})q^{5}+(-4+2\zeta_{6})q^{7}+\cdots\)
2028.2.q.b	$2028$	$2$	2028.q	13.e	$6$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.b.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-2+4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.c	$2028$	$2$	2028.q	13.e	$6$	$2$	$1$	$16.194$	\(\Q(\sqrt{-3}) \)	None					156.2.b.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2028.2.q.d	$2028$	$2$	2028.q	13.e	$6$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.a.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{2} q^{3}-\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots\)
2028.2.q.e	$2028$	$2$	2028.q	13.e	$6$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.b.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{2} q^{3}+\beta_{3} q^{5}-2\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots\)
2028.2.q.f	$2028$	$2$	2028.q	13.e	$6$	$4$	$2$	$16.194$	\(\Q(\sqrt{-3}, \sqrt{-43})\)	None					156.2.q.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2028.2.q.g	$2028$	$2$	2028.q	13.e	$6$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.i.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{3}+2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
2028.2.q.h	$2028$	$2$	2028.q	13.e	$6$	$4$	$2$	$16.194$	\(\Q(\zeta_{12})\)	None					156.2.a.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_{2} q^{3}+2\beta_{3} q^{5}+\beta_1 q^{7}+(\beta_{2}-1)q^{9}+\cdots\)
2028.2.q.i	$2028$	$2$	2028.q	13.e	$6$	$12$	$6$	$16.194$	12.0.\(\cdots\).1	None		✓			2028.2.a.k	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{7})q^{3}+(-2\beta _{2}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
2028.2.q.j	$2028$	$2$	2028.q	13.e	$6$	$12$	$6$	$16.194$	12.0.\(\cdots\).1	None		✓			2028.2.a.i	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{3}+(-\beta _{2}-\beta _{8}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)