Space of modular forms of level 28, weight 12, and Character 28.e

• Label: 28.12.e
• Level: $28$
• Weight: $12$
• Character orbit: 28.e
• Rep. character: $\chi_{28}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(28, [\chi])\).

	Total	New	Old
Modular forms	94	14	80
Cusp forms	82	14	68
Eisenstein series	12	0	12

Trace form

14 * q + 243 * q^3 + 3719 * q^5 - 83356 * q^7 - 294938 * q^9 - 72905 * q^11 - 2193572 * q^13 + 1372294 * q^15 - 261533 * q^17 + 13374085 * q^19 - 13411307 * q^21 - 11167331 * q^23 - 2989084 * q^25 - 342323586 * q^27 - 30906484 * q^29 - 256257785 * q^31 + 128137973 * q^33 - 64940645 * q^35 + 83028715 * q^37 - 895728890 * q^39 + 979709316 * q^41 + 172751992 * q^43 - 70094950 * q^45 - 1276652103 * q^47 + 766357550 * q^49 - 1686965119 * q^51 + 521040303 * q^53 + 511903374 * q^55 + 13547111298 * q^57 + 5829711443 * q^59 + 1751145379 * q^61 + 17130494766 * q^63 - 412905234 * q^65 + 6447767179 * q^67 - 31462866478 * q^69 - 24715621280 * q^71 + 10539220351 * q^73 - 3842509652 * q^75 + 188362769 * q^77 - 16799842619 * q^79 - 84787948175 * q^81 + 37081512184 * q^83 - 64191070650 * q^85 - 12573329666 * q^87 + 36562951407 * q^89 + 104005007176 * q^91 + 83041323253 * q^93 - 30995705909 * q^95 - 96236737820 * q^97 - 323900282804 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(28, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
28.12.e.a	$28$	$12$	28.e	7.c	$3$	$14$	$7$	$21.514$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓	✓	28.12.e.a	$2$	$0$	\(0\)	\(243\)	\(3719\)	\(-83356\)	$2^{42}\cdot 3^{5}\cdot 7^{11}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(35\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(531-531\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(28, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)