Space of modular forms of level 1224, weight 4, and Character 1224.c

• Label: 1224.4.c
• Level: $1224$
• Weight: $4$
• Character orbit: 1224.c
• Rep. character: $\chi_{1224}(577,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $8$
• Sturm bound: $864$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1224.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(864\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

	Total	New	Old
Modular forms	664	68	596
Cusp forms	632	68	564
Eisenstein series	32	0	32

Trace form

68 * q - 40 * q^13 + 16 * q^17 + 24 * q^19 - 1684 * q^25 + 208 * q^35 - 424 * q^43 + 504 * q^47 - 4028 * q^49 + 1304 * q^53 + 1176 * q^55 - 1160 * q^59 + 1680 * q^67 + 240 * q^77 + 1744 * q^83 + 2688 * q^85 + 2096 * q^89

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1224.4.c.a	$1224$	$4$	1224.c	17.b	$2$	$2$	$2$	$72.218$	\(\Q(\sqrt{-1}) \)	None					408.4.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+9\beta q^{5}-7\beta q^{7}+16\beta q^{11}+82 q^{13}+\cdots\)
1224.4.c.b	$1224$	$4$	1224.c	17.b	$2$	$6$	$6$	$72.218$	6.0.\(\cdots\).1	None					408.4.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
1224.4.c.c	$1224$	$4$	1224.c	17.b	$2$	$6$	$6$	$72.218$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					136.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1224.4.c.d	$1224$	$4$	1224.c	17.b	$2$	$6$	$6$	$72.218$	6.0.\(\cdots\).1	None					408.4.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}-\beta _{4})q^{5}+(-2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1224.4.c.e	$1224$	$4$	1224.c	17.b	$2$	$8$	$8$	$72.218$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					136.4.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots\)
1224.4.c.f	$1224$	$4$	1224.c	17.b	$2$	$12$	$12$	$72.218$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					408.4.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{19}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+(\beta _{4}-\beta _{5})q^{7}+(-\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
1224.4.c.g	$1224$	$4$	1224.c	17.b	$2$	$14$	$14$	$72.218$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			1224.4.c.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{6}q^{7}+(-\beta _{1}-\beta _{11})q^{11}+\cdots\)
1224.4.c.h	$1224$	$4$	1224.c	17.b	$2$	$14$	$14$	$72.218$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			1224.4.c.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{6}q^{7}+(-\beta _{1}-\beta _{11})q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)