Space of modular forms of level 400, weight 3, and Character 400.bk

• Label: 400.3.bk
• Level: $400$
• Weight: $3$
• Character orbit: 400.bk
• Rep. character: $\chi_{400}(11,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $944$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bk (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(400, [\chi])\).

	Total	New	Old
Modular forms	976	976	0
Cusp forms	944	944	0
Eisenstein series	32	32	0

Trace form

944 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 - 32 * q^7 + 12 * q^8 - 26 * q^10 - 6 * q^11 - 54 * q^12 - 6 * q^13 - 30 * q^14 - 6 * q^16 - 12 * q^17 - 32 * q^18 - 6 * q^19 + 34 * q^20 - 60 * q^21 + 106 * q^22 - 12 * q^23 - 16 * q^24 - 116 * q^26 - 42 * q^27 - 102 * q^28 - 6 * q^29 - 62 * q^30 + 124 * q^32 - 12 * q^33 + 170 * q^34 - 160 * q^35 - 370 * q^36 - 6 * q^37 + 400 * q^38 - 12 * q^39 - 500 * q^40 - 342 * q^42 + 112 * q^43 + 204 * q^44 - 76 * q^45 + 10 * q^46 - 372 * q^48 + 5904 * q^49 - 126 * q^50 + 20 * q^51 - 376 * q^52 - 6 * q^53 - 150 * q^54 - 272 * q^55 - 300 * q^56 + 346 * q^58 - 6 * q^59 - 1720 * q^60 - 6 * q^61 - 274 * q^62 + 264 * q^64 + 48 * q^65 - 440 * q^66 - 438 * q^67 - 260 * q^68 + 30 * q^69 - 364 * q^70 - 12 * q^71 - 682 * q^72 - 236 * q^74 + 278 * q^75 - 316 * q^76 - 300 * q^77 + 366 * q^78 - 2 * q^80 + 1824 * q^81 - 432 * q^82 - 166 * q^83 + 80 * q^84 + 42 * q^85 - 606 * q^86 - 908 * q^87 - 664 * q^88 + 330 * q^90 - 300 * q^91 - 872 * q^92 - 52 * q^93 + 378 * q^94 + 894 * q^96 - 12 * q^97 - 580 * q^98 - 304 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(400, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
400.3.bk.a	$400$	$3$	400.bk	400.ak	$20$	$944$	$118$	$10.899$		None		✓	✓	✓	400.3.bk.a	$4$	$0$	\(-6\)	\(-6\)	\(-8\)	\(-32\)		$\mathrm{SU}(2)[C_{20}]$