Space of modular forms of level 272, weight 4, and Character 272.b

• Label: 272.4.b
• Level: $272$
• Weight: $4$
• Character orbit: 272.b
• Rep. character: $\chi_{272}(33,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $6$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	272.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(272, [\chi])\).

	Total	New	Old
Modular forms	114	28	86
Cusp forms	102	26	76
Eisenstein series	12	2	10

Trace form

26 * q - 238 * q^9 - 48 * q^13 + 8 * q^15 - 26 * q^17 - 136 * q^19 + 52 * q^21 - 574 * q^25 + 204 * q^33 + 520 * q^35 - 256 * q^43 - 840 * q^47 - 982 * q^49 - 904 * q^51 + 676 * q^53 - 1288 * q^55 - 432 * q^59 + 440 * q^67 + 60 * q^69 + 1196 * q^77 + 1590 * q^81 - 2576 * q^83 - 720 * q^85 + 4232 * q^87 - 832 * q^89 - 916 * q^93

Decomposition of \(S_{4}^{\mathrm{new}}(272, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.4.b.a	$272$	$4$	272.b	17.b	$2$	$2$	$2$	$16.049$	\(\Q(\sqrt{-2}) \)	None					34.4.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}-\beta q^{5}-3\beta q^{7}-5q^{9}-20\beta q^{11}+\cdots\)
272.4.b.b	$272$	$4$	272.b	17.b	$2$	$2$	$2$	$16.049$	\(\Q(\sqrt{-1}) \)	None					34.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-4\beta q^{5}+17\beta q^{7}+23 q^{9}+\cdots\)
272.4.b.c	$272$	$4$	272.b	17.b	$2$	$4$	$4$	$16.049$	\(\Q(\sqrt{-42 +2 \sqrt{433}})\)	None					68.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-15+\cdots)q^{9}+\cdots\)
272.4.b.d	$272$	$4$	272.b	17.b	$2$	$4$	$4$	$16.049$	\(\Q(\sqrt{-37 +3 \sqrt{33}})\)	None					17.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
272.4.b.e	$272$	$4$	272.b	17.b	$2$	$6$	$6$	$16.049$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					136.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
272.4.b.f	$272$	$4$	272.b	17.b	$2$	$8$	$8$	$16.049$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None			✓		136.4.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)