Space of modular forms of level 528, weight 3, and Character 528.bf

• Label: 528.3.bf
• Level: $528$
• Weight: $3$
• Character orbit: 528.bf
• Rep. character: $\chi_{528}(145,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	528.bf (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(528, [\chi])\).

	Total	New	Old
Modular forms	816	96	720
Cusp forms	720	96	624
Eisenstein series	96	0	96

Trace form

96 * q - 72 * q^9 + 16 * q^11 + 32 * q^23 - 104 * q^25 - 24 * q^33 - 480 * q^35 - 144 * q^37 + 80 * q^41 + 144 * q^47 - 56 * q^49 + 208 * q^53 + 464 * q^55 - 256 * q^59 + 160 * q^67 + 320 * q^71 + 280 * q^73 + 288 * q^75 + 208 * q^77 + 160 * q^79 - 216 * q^81 + 400 * q^83 + 80 * q^85 + 160 * q^89 - 336 * q^91 - 144 * q^93 - 800 * q^95 + 64 * q^97 - 192 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(528, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
528.3.bf.a	$528$	$3$	528.bf	11.d	$10$	$16$	$4$	$14.387$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					132.3.l.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(30\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{7}q^{3}+(-\beta _{1}+\beta _{3}-2\beta _{11}-2\beta _{12}+\cdots)q^{5}+\cdots\)
528.3.bf.b	$528$	$3$	528.bf	11.d	$10$	$16$	$4$	$14.387$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					33.3.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(30\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{10}q^{3}+(-\beta _{5}+\beta _{11}+\beta _{13})q^{5}+\cdots\)
528.3.bf.c	$528$	$3$	528.bf	11.d	$10$	$16$	$4$	$14.387$	16.0.\(\cdots\).7	None					66.3.f.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-60\)	$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{9}q^{3}+(1-\beta _{2}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
528.3.bf.d	$528$	$3$	528.bf	11.d	$10$	$48$	$12$	$14.387$		None			✓		264.3.x.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(528, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)