Space of modular forms of level 1428, weight 2, and Character 1428.cc

• Label: 1428.2.cc
• Level: $1428$
• Weight: $2$
• Character orbit: 1428.cc
• Rep. character: $\chi_{1428}(361,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.cc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

	Total	New	Old
Modular forms	1200	96	1104
Cusp forms	1104	96	1008
Eisenstein series	96	0	96

Trace form

96 * q + 4 * q^5 + 4 * q^7 + 4 * q^11 + 32 * q^13 - 8 * q^17 + 8 * q^23 - 8 * q^31 + 16 * q^33 + 24 * q^35 + 32 * q^41 - 4 * q^45 - 8 * q^47 + 16 * q^57 + 12 * q^61 + 4 * q^63 - 48 * q^65 - 8 * q^67 - 64 * q^69 - 16 * q^71 + 20 * q^73 + 16 * q^75 + 12 * q^79 + 48 * q^81 - 80 * q^85 - 8 * q^89 - 4 * q^91 - 76 * q^95 + 56 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1428.2.cc.a	$1428$	$2$	1428.cc	119.n	$12$	$8$	$2$	$11.403$	\(\Q(\zeta_{24})\)	None		✓			1428.2.cc.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{7}q^{5}+\cdots\)
1428.2.cc.b	$1428$	$2$	1428.cc	119.n	$12$	$16$	$4$	$11.403$	16.0.\(\cdots\).1	None		✓			1428.2.cc.b	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(24\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{5}+\beta _{14})q^{3}+(\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots\)
1428.2.cc.c	$1428$	$2$	1428.cc	119.n	$12$	$72$	$18$	$11.403$		None		✓	✓		1428.2.cc.c	$4$	$0$	\(0\)	\(0\)	\(12\)	\(-20\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 2}\)