Space of modular forms of level 15, weight 11, and Character 15.f

• Label: 15.11.f
• Level: $15$
• Weight: $11$
• Character orbit: 15.f
• Rep. character: $\chi_{15}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $22$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(22\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(15, [\chi])\).

	Total	New	Old
Modular forms	44	20	24
Cusp forms	36	20	16
Eisenstein series	8	0	8

Trace form

20 * q - 64 * q^2 + 10676 * q^5 - 4860 * q^6 + 10604 * q^7 - 39948 * q^8 + 153704 * q^10 + 32080 * q^11 - 620136 * q^12 - 69352 * q^13 + 662904 * q^15 - 3111700 * q^16 + 347360 * q^17 - 1259712 * q^18 + 24132564 * q^20 + 1448280 * q^21 - 27255980 * q^22 - 30995704 * q^23 + 36824936 * q^25 + 80977840 * q^26 - 104897636 * q^28 - 6436584 * q^30 - 8846480 * q^31 - 81249676 * q^32 + 86048244 * q^33 + 91578920 * q^35 + 177540660 * q^36 - 27635896 * q^37 + 44187744 * q^38 - 887009352 * q^40 + 149264920 * q^41 + 442105452 * q^42 + 675552392 * q^43 - 183996684 * q^45 - 1916100680 * q^46 - 257112832 * q^47 + 1182772368 * q^48 + 909704384 * q^50 - 711183240 * q^51 + 1397512520 * q^52 - 152646064 * q^53 - 1181518004 * q^55 + 1735516800 * q^56 + 342507528 * q^57 - 1947576252 * q^58 - 1084331124 * q^60 + 2582791000 * q^61 - 969372632 * q^62 + 208718532 * q^63 + 7250334488 * q^65 - 1968290280 * q^66 - 6731030200 * q^67 - 12869460704 * q^68 + 7421027700 * q^70 + 7511442640 * q^71 + 786296484 * q^72 + 1660222316 * q^73 + 72454824 * q^75 + 9998646360 * q^76 - 13264676792 * q^77 - 5574993480 * q^78 - 15692039116 * q^80 - 7748409780 * q^81 + 27089146528 * q^82 + 30753878864 * q^83 - 2653017808 * q^85 - 46532117120 * q^86 + 3048661476 * q^87 + 5813201532 * q^88 + 8161910244 * q^90 + 14175275920 * q^91 + 30045377384 * q^92 - 6062778072 * q^93 - 58265269776 * q^95 - 18513718020 * q^96 - 32149992820 * q^97 + 54432471592 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.11.f.a	$15$	$11$	15.f	5.c	$4$	$20$	$10$	$9.530$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	15.11.f.a	$2$	$0$	\(-64\)	\(0\)	\(10676\)	\(10604\)	$2^{21}\cdot 3^{34}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-3-3\beta _{2}-\beta _{3})q^{2}+\beta _{6}q^{3}+(451\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(15, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)