Space of modular forms of level 279, weight 3, and Character 279.d

• Label: 279.3.d
• Level: $279$
• Weight: $3$
• Character orbit: 279.d
• Rep. character: $\chi_{279}(154,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	279.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(279, [\chi])\).

	Total	New	Old
Modular forms	68	27	41
Cusp forms	60	25	35
Eisenstein series	8	2	6

Trace form

\( 25 q + 2 q^{2} + 46 q^{4} - 4 q^{5} - 16 q^{7} + 25 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(279, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
279.3.d.a	$279$	$3$	279.d	31.b	$2$	$2$	$2$	$7.602$	\(\Q(\sqrt{-26}) \)	None					31.3.b.a	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(16\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-3q^{4}-2q^{5}+8q^{7}-7q^{8}+\cdots\)
279.3.d.b	$279$	$3$	279.d	31.b	$2$	$2$	$2$	$7.602$	\(\Q(\sqrt{-3}) \)	None					93.3.d.a	$2$	$0$	\(6\)	\(0\)	\(12\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{2}+5q^{4}+6q^{5}+2q^{7}+3q^{8}+\cdots\)
279.3.d.c	$279$	$3$	279.d	31.b	$2$	$3$	$3$	$7.602$	3.3.837.1	\(\Q(\sqrt{-31}) \)	✓				31.3.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots\)
279.3.d.d	$279$	$3$	279.d	31.b	$2$	$4$	$4$	$7.602$	\(\Q(\sqrt{3}, \sqrt{-53})\)	None		✓			279.3.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}-4q^{7}-5\beta _{1}q^{8}+\cdots\)
279.3.d.e	$279$	$3$	279.d	31.b	$2$	$6$	$6$	$7.602$	6.6.1389928896.1	\(\Q(\sqrt{-31}) \)	✓	✓			279.3.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+(4+\beta _{4}-\beta _{5})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
279.3.d.f	$279$	$3$	279.d	31.b	$2$	$8$	$8$	$7.602$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None			✓		93.3.d.b	$2$	$0$	\(-6\)	\(0\)	\(-12\)	\(-20\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(279, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(279, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)