Space of modular forms of level 100, weight 6, and Character 100.i

• Label: 100.6.i
• Level: $100$
• Weight: $6$
• Character orbit: 100.i
• Rep. character: $\chi_{100}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$100 = 2^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	100.i (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$25$
Character field:			$\Q(\zeta_{10})$
Newform subspaces:			$1$
Sturm bound:			$90$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(100, [\chi])$.

	Total	New	Old
Modular forms	312	48	264
Cusp forms	288	48	240
Eisenstein series	24	0	24

Trace form

48 * q - 135 * q^5 + 872 * q^9 + 5 * q^11 + 20 * q^15 - 955 * q^17 + 1912 * q^19 + 4818 * q^21 - 1420 * q^23 - 8605 * q^25 - 13800 * q^27 - 4408 * q^29 - 5532 * q^31 + 28465 * q^33 - 2165 * q^35 + 3540 * q^37 - 9938 * q^39 + 16383 * q^41 + 81600 * q^45 + 58745 * q^47 - 74126 * q^49 - 68014 * q^51 - 31320 * q^53 - 9065 * q^55 - 116271 * q^59 - 20184 * q^61 + 93820 * q^63 + 84335 * q^65 + 45395 * q^67 + 84806 * q^69 + 174099 * q^71 - 185460 * q^73 - 333405 * q^75 - 217020 * q^77 + 122216 * q^79 + 41997 * q^81 + 421590 * q^83 + 30775 * q^85 - 313155 * q^87 - 40897 * q^89 - 58608 * q^91 + 218670 * q^95 + 185675 * q^97 + 532180 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(100, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.6.i.a	$100$	$6$	100.i	25.e	$10$	$48$	$12$	$16.038$		None		✓	✓	✓	100.6.i.a	$2$	$0$	$0$	$0$	$-135$	$0$		$\mathrm{SU}(2)[C_{10}]$

Decomposition of $S_{6}^{\mathrm{old}}(100, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(100, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(25, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(50, [\chi])$$^{\oplus 2}$