Space of modular forms of level 279, weight 6, and trivial character

• Label: 279.6.a
• Level: $279$
• Weight: $6$
• Character orbit: 279.a
• Rep. character: $\chi_{279}(1,\cdot)$
• Character field: $\Q$
• Dimension: $63$
• Newform subspaces: $8$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	279.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(279))\).

	Total	New	Old
Modular forms	164	63	101
Cusp forms	156	63	93
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(31\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(38\)	\(10\)	\(28\)		\(36\)	\(10\)	\(26\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(44\)	\(16\)	\(28\)		\(42\)	\(16\)	\(26\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(44\)	\(20\)	\(24\)		\(42\)	\(20\)	\(22\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(38\)	\(17\)	\(21\)		\(36\)	\(17\)	\(19\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(76\)	\(27\)	\(49\)		\(72\)	\(27\)	\(45\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(88\)	\(36\)	\(52\)		\(84\)	\(36\)	\(48\)		\(4\)	\(0\)	\(4\)

Trace form

63 * q - 10 * q^2 + 1002 * q^4 - 44 * q^5 - 20 * q^7 - 147 * q^8 - 323 * q^10 - 820 * q^11 - 540 * q^13 - 183 * q^14 + 19162 * q^16 + 4728 * q^17 + 2372 * q^19 - 743 * q^20 - 1816 * q^22 + 2414 * q^23 + 39911 * q^25 + 9006 * q^26 - 6489 * q^28 + 16664 * q^29 + 2883 * q^31 - 4254 * q^32 + 10684 * q^34 - 12260 * q^35 - 2618 * q^37 - 23503 * q^38 - 15468 * q^40 - 11804 * q^41 + 10530 * q^43 + 50624 * q^44 + 1874 * q^46 + 16708 * q^47 + 153973 * q^49 - 12287 * q^50 + 2824 * q^52 + 53814 * q^53 + 15292 * q^55 - 16220 * q^56 + 76620 * q^58 + 11268 * q^59 - 19480 * q^61 - 15376 * q^62 + 230933 * q^64 - 23626 * q^65 + 17652 * q^67 + 255902 * q^68 + 81501 * q^70 + 89708 * q^71 + 26986 * q^73 - 61822 * q^74 + 377727 * q^76 + 252596 * q^77 + 76102 * q^79 - 30975 * q^80 + 344059 * q^82 + 95832 * q^83 + 114702 * q^85 - 193294 * q^86 + 510762 * q^88 - 310396 * q^89 + 215914 * q^91 + 199952 * q^92 + 197252 * q^94 + 233208 * q^95 + 32784 * q^97 + 728133 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(279))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	31
279.6.a.a	$279$	$6$	279.a	1.a	$1$	$4$	$4$	$44.747$	4.4.3911701.1	None	✓				93.6.a.a	$1$	$1$	\(3\)	\(0\)	\(42\)	\(-284\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{2}+(13-4\beta _{1}+5\beta _{2}+\cdots)q^{4}+\cdots\)
279.6.a.b	$279$	$6$	279.a	1.a	$1$	$5$	$5$	$44.747$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				93.6.a.b	$1$	$1$	\(-9\)	\(0\)	\(-36\)	\(108\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(11+\beta _{2}-\beta _{4})q^{4}+\cdots\)
279.6.a.c	$279$	$6$	279.a	1.a	$1$	$5$	$5$	$44.747$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				31.6.a.a	$1$	$0$	\(9\)	\(0\)	\(72\)	\(-108\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(12-4\beta _{1}+3\beta _{3}+\beta _{4})q^{4}+\cdots\)
279.6.a.d	$279$	$6$	279.a	1.a	$1$	$7$	$7$	$44.747$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				93.6.a.c	$1$	$0$	\(3\)	\(0\)	\(64\)	\(-88\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(14+\beta _{2})q^{4}+(9+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
279.6.a.e	$279$	$6$	279.a	1.a	$1$	$8$	$8$	$44.747$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		93.6.a.d	$1$	$0$	\(-9\)	\(0\)	\(-58\)	\(304\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(24+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
279.6.a.f	$279$	$6$	279.a	1.a	$1$	$8$	$8$	$44.747$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		31.6.a.b	$1$	$1$	\(-7\)	\(0\)	\(-128\)	\(88\)		$-$	$-$	$+$	$2^{2}\cdot 3^{2}\cdot 5\cdot 13$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(19-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
279.6.a.g	$279$	$6$	279.a	1.a	$1$	$10$	$10$	$44.747$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	279.6.a.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-216\)		$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(11+\beta _{2})q^{4}+\beta _{5}q^{5}+(-22+\cdots)q^{7}+\cdots\)
279.6.a.h	$279$	$6$	279.a	1.a	$1$	$16$	$16$	$44.747$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	279.6.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(176\)		$+$	$-$	$-$	$2^{5}\cdot 3^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(19+\beta _{2})q^{4}+\beta _{9}q^{5}+(11+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(279))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(279)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)