Space of modular forms of level 15, weight 10, and Character 15.e

• Label: 15.10.e
• Level: $15$
• Weight: $10$
• Character orbit: 15.e
• Rep. character: $\chi_{15}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(15, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

32 * q - 150 * q^3 - 4548 * q^6 - 9760 * q^7 - 39820 * q^10 + 191940 * q^12 + 114260 * q^13 - 40230 * q^15 - 1494724 * q^16 + 994800 * q^18 + 592212 * q^21 + 308260 * q^22 + 5808020 * q^25 + 4786830 * q^27 - 12953300 * q^28 - 17343060 * q^30 + 16124104 * q^31 + 19638120 * q^33 - 48943956 * q^36 - 35578660 * q^37 + 144132840 * q^40 + 46648260 * q^42 - 118721020 * q^43 - 129688380 * q^45 + 3145024 * q^46 + 275395140 * q^48 - 64226868 * q^51 - 157103680 * q^52 + 144539740 * q^55 + 48163500 * q^57 - 209634300 * q^58 - 140815620 * q^60 + 63607744 * q^61 + 89858580 * q^63 + 358931400 * q^66 + 153311540 * q^67 + 420519420 * q^70 - 1534046760 * q^72 + 628070360 * q^73 + 138090210 * q^75 - 2457023472 * q^76 - 403337880 * q^78 + 2250542952 * q^81 + 4138031440 * q^82 + 108907340 * q^85 - 2878139760 * q^87 - 595851300 * q^88 + 693868920 * q^90 - 4369040216 * q^91 - 293672640 * q^93 + 7291125636 * q^96 + 3987642200 * q^97

Decomposition of \(S_{10}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.10.e.a	$15$	$10$	15.e	15.e	$4$	$32$	$16$	$7.726$		None		✓	✓	✓	15.10.e.a	$4$	$0$	\(0\)	\(-150\)	\(0\)	\(-9760\)		$\mathrm{SU}(2)[C_{4}]$