Space of modular forms of level 1100, weight 2, and Character 1100.q

• Label: 1100.2.q
• Level: $1100$
• Weight: $2$
• Character orbit: 1100.q
• Rep. character: $\chi_{1100}(221,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(360\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1100, [\chi])\).

	Total	New	Old
Modular forms	744	96	648
Cusp forms	696	96	600
Eisenstein series	48	0	48

Trace form

96 * q - 2 * q^3 + 6 * q^5 - 22 * q^9 + 2 * q^11 + 12 * q^13 - 37 * q^15 - 8 * q^17 - 12 * q^21 + 26 * q^23 + 14 * q^25 + 55 * q^27 + 24 * q^29 - 6 * q^31 - 2 * q^33 + 10 * q^35 - 24 * q^37 - 24 * q^39 + 12 * q^41 - 72 * q^43 - 8 * q^45 + 34 * q^47 + 64 * q^49 + 4 * q^51 - 14 * q^53 - 3 * q^55 - 16 * q^57 - 9 * q^59 + 20 * q^61 - 28 * q^63 + 32 * q^65 + 25 * q^67 + 77 * q^69 + 8 * q^71 - 12 * q^73 + 71 * q^75 + 16 * q^79 - 33 * q^81 + 76 * q^83 - 48 * q^85 - 66 * q^87 - 16 * q^89 + 60 * q^91 + 16 * q^93 + 12 * q^95 + 24 * q^97 - 34 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.2.q.a	$1100$	$2$	1100.q	25.d	$5$	$44$	$11$	$8.784$		None		✓			1100.2.q.a	$2$	$0$	\(0\)	\(-2\)	\(9\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$
1100.2.q.b	$1100$	$2$	1100.q	25.d	$5$	$52$	$13$	$8.784$		None		✓	✓		1100.2.q.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)