Space of modular forms of level 15, weight 8, and Character 15.e

• Label: 15.8.e
• Level: $15$
• Weight: $8$
• Character orbit: 15.e
• Rep. character: $\chi_{15}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(15, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7 - 3180 * q^10 - 2028 * q^12 + 16848 * q^13 + 37560 * q^15 - 68868 * q^16 - 106560 * q^18 + 84144 * q^21 + 166020 * q^22 - 275760 * q^25 - 264168 * q^27 + 602028 * q^28 + 892380 * q^30 - 208992 * q^31 - 877800 * q^33 - 256212 * q^36 - 635616 * q^37 - 1574040 * q^40 + 1219380 * q^42 + 1397328 * q^43 + 570240 * q^45 + 2787168 * q^46 - 476796 * q^48 - 4028016 * q^51 - 6426336 * q^52 + 2324880 * q^55 + 8457264 * q^57 + 986340 * q^58 + 2037900 * q^60 + 12157968 * q^61 - 1973952 * q^63 - 25406040 * q^66 - 16720176 * q^67 - 13165860 * q^70 + 36245880 * q^72 + 4059528 * q^73 + 11226120 * q^75 + 37968816 * q^76 - 26156280 * q^78 - 31289976 * q^81 - 53633520 * q^82 - 34181760 * q^85 + 44480160 * q^87 + 74717340 * q^88 + 71623080 * q^90 + 67599648 * q^91 - 58742592 * q^93 - 103105308 * q^96 - 75148056 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.8.e.a	$15$	$8$	15.e	15.e	$4$	$24$	$12$	$4.686$		None		✓	✓	✓	15.8.e.a	$4$	$0$	\(0\)	\(24\)	\(0\)	\(1344\)		$\mathrm{SU}(2)[C_{4}]$