Space of modular forms of level 279, weight 2, and Character 279.y

• Label: 279.2.y
• Level: $279$
• Weight: $2$
• Character orbit: 279.y
• Rep. character: $\chi_{279}(10,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.y (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(279, [\chi])\).

	Total	New	Old
Modular forms	288	112	176
Cusp forms	224	96	128
Eisenstein series	64	16	48

Trace form

96 * q + 6 * q^2 - 22 * q^4 + 3 * q^5 - 18 * q^7 - 5 * q^8 + 2 * q^10 + 19 * q^11 - 13 * q^13 + 8 * q^14 - 26 * q^16 + 20 * q^17 - 38 * q^19 - 5 * q^20 + 37 * q^22 - 5 * q^23 - 21 * q^25 - 31 * q^26 - 54 * q^28 - 26 * q^29 + 19 * q^31 + 6 * q^32 + 44 * q^34 - 3 * q^35 - 6 * q^37 - 14 * q^38 + 43 * q^40 + 12 * q^41 + 11 * q^43 - q^44 + 38 * q^46 + 22 * q^47 - 40 * q^49 - 53 * q^50 + 17 * q^52 - 16 * q^53 - 63 * q^55 + 8 * q^56 - 63 * q^58 + 52 * q^59 - 108 * q^61 - 13 * q^62 - 17 * q^64 - 94 * q^65 + 29 * q^67 - 96 * q^68 + 20 * q^70 + 2 * q^71 - 56 * q^73 - 17 * q^74 - 52 * q^76 - 34 * q^77 - 56 * q^79 + 56 * q^80 + 6 * q^82 + 44 * q^83 + 21 * q^85 + 144 * q^86 + 83 * q^88 + 69 * q^89 + 74 * q^91 + 176 * q^92 - 36 * q^94 + 80 * q^95 + 9 * q^97 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(279, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
279.2.y.a	$279$	$2$	279.y	31.g	$15$	$8$	$1$	$2.228$	\(\Q(\zeta_{15})\)	\(\Q(\sqrt{-3}) \)		✓			279.2.y.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{15}]$	\(q+(2\zeta_{15}^{2}+2\zeta_{15}^{7})q^{4}+(-3+2\zeta_{15}+\cdots)q^{7}+\cdots\)
279.2.y.b	$279$	$2$	279.y	31.g	$15$	$16$	$2$	$2.228$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					93.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{7}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
279.2.y.c	$279$	$2$	279.y	31.g	$15$	$16$	$2$	$2.228$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(6\)	\(0\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\beta _{1}-\beta _{4}+\beta _{5}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{2}+\cdots\)
279.2.y.d	$279$	$2$	279.y	31.g	$15$	$24$	$3$	$2.228$		None					93.2.m.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-1\)		$\mathrm{SU}(2)[C_{15}]$
279.2.y.e	$279$	$2$	279.y	31.g	$15$	$32$	$4$	$2.228$		None		✓	✓		279.2.y.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(279, [\chi])\) into lower level spaces

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