Space of modular forms of level 100, weight 2, and Character 100.g

• Label: 100.2.g
• Level: $100$
• Weight: $2$
• Character orbit: 100.g
• Rep. character: $\chi_{100}(21,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

12 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 3 * q^9 - 5 * q^11 - 2 * q^13 + 18 * q^15 + q^17 - 8 * q^19 + 2 * q^21 - 6 * q^23 - 26 * q^25 - 34 * q^27 - 18 * q^29 + 12 * q^31 - 35 * q^33 - 3 * q^35 + 13 * q^37 + 22 * q^39 - 23 * q^41 + 50 * q^43 + 71 * q^45 + q^47 + 34 * q^49 + 14 * q^51 + 21 * q^53 + 5 * q^55 + 72 * q^57 + 9 * q^59 - 26 * q^61 - 32 * q^63 - 18 * q^65 - 37 * q^67 - 44 * q^69 + 21 * q^71 + 18 * q^73 - 73 * q^75 - 60 * q^77 - 24 * q^79 + 18 * q^81 - 46 * q^83 - 16 * q^85 + 57 * q^87 - 2 * q^89 - 32 * q^91 + 22 * q^93 + 6 * q^95 - 7 * q^97 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.2.g.a	$100$	$2$	100.g	25.d	$5$	$12$	$3$	$0.799$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	100.2.g.a	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

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