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

• Label: 100.2.i
• Level: $100$
• Weight: $2$
• Character orbit: 100.i
• Rep. character: $\chi_{100}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• 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.i (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
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	8	64
Cusp forms	48	8	40
Eisenstein series	24	0	24

Trace form

8 * q + 5 * q^5 + 2 * q^9 + 5 * q^11 - 20 * q^15 - 5 * q^17 - 8 * q^19 - 2 * q^21 - 20 * q^23 - 5 * q^25 - 8 * q^29 - 12 * q^31 + 15 * q^33 - 5 * q^35 - 10 * q^37 + 22 * q^39 + 13 * q^41 + 10 * q^45 + 45 * q^47 + 14 * q^49 - 14 * q^51 + 30 * q^53 + 35 * q^55 + 9 * q^59 + 16 * q^61 + 20 * q^63 - 25 * q^65 - 5 * q^67 - 14 * q^69 - q^71 - 60 * q^73 - 5 * q^75 - 20 * q^77 - 24 * q^79 - 3 * q^81 - 10 * q^83 - 5 * q^85 - 55 * q^87 - 37 * q^89 + 32 * q^91 + 30 * q^95 + 25 * q^97 + 20 * 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.i.a	$100$	$2$	100.i	25.e	$10$	$8$	$2$	$0.799$	8.0.58140625.2	None		✓	✓	✓	100.2.i.a	$2$	$0$	\(0\)	\(0\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)

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

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