Space of modular forms of level 100, weight 4, and Character 100.i

• Label: 100.4.i
• Level: $100$
• Weight: $4$
• Character orbit: 100.i
• Rep. character: $\chi_{100}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(100, [\chi])\).

	Total	New	Old
Modular forms	192	32	160
Cusp forms	168	32	136
Eisenstein series	24	0	24

Trace form

32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.4.i.a	$100$	$4$	100.i	25.e	$10$	$32$	$8$	$5.900$		None		✓	✓	✓	100.4.i.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)