Space of modular forms of level 15, weight 5, and Character 15.f

• Label: 15.5.f
• Level: $15$
• Weight: $5$
• Character orbit: 15.f
• Rep. character: $\chi_{15}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

	Total	New	Old
Modular forms	20	8	12
Cusp forms	12	8	4
Eisenstein series	8	0	8

Trace form

8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.5.f.a	$15$	$5$	15.f	5.c	$4$	$8$	$4$	$1.551$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	15.5.f.a	$2$	$0$	\(0\)	\(0\)	\(-84\)	\(20\)	$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(15, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)