Space of modular forms of level 15, weight 4, and Character 15.e

• Label: 15.4.e
• Level: $15$
• Weight: $4$
• Character orbit: 15.e
• Rep. character: $\chi_{15}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(15, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.4.e.a	$15$	$4$	15.e	15.e	$4$	$8$	$4$	$0.885$	8.0.\(\cdots\).8	None		✓	✓	✓	15.4.e.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)