Space of modular forms of level 3528, weight 3, and Character 3528.d

• Label: 3528.3.d
• Level: $3528$
• Weight: $3$
• Character orbit: 3528.d
• Rep. character: $\chi_{3528}(1961,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $12$
• Sturm bound: $2016$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3528.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2016\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3528, [\chi])\).

	Total	New	Old
Modular forms	1408	82	1326
Cusp forms	1280	82	1198
Eisenstein series	128	0	128

Trace form

\( 82 q + 32 q^{19} - 338 q^{25} + 40 q^{31} - 84 q^{37} + 16 q^{43} - 48 q^{55} + 84 q^{61} - 208 q^{67} + 224 q^{73} + 56 q^{79} - 44 q^{85} + 192 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3528, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3528.3.d.a	$3528$	$3$	3528.d	3.b	$2$	$2$	$2$	$96.131$	\(\Q(\sqrt{-2}) \)	None					72.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}+4\beta q^{11}+8q^{13}+7\beta q^{17}+\cdots\)
3528.3.d.b	$3528$	$3$	3528.d	3.b	$2$	$4$	$4$	$96.131$	\(\Q(\zeta_{8})\)	None		✓			3528.3.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-\beta_{2} q^{11}-2\beta_{3} q^{13}+\beta_1 q^{17}+\cdots\)
3528.3.d.c	$3528$	$3$	3528.d	3.b	$2$	$4$	$4$	$96.131$	\(\Q(\zeta_{8})\)	None		✓			3528.3.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-6\beta_{2} q^{11}-17\beta_{3} q^{13}+\cdots\)
3528.3.d.d	$3528$	$3$	3528.d	3.b	$2$	$4$	$4$	$96.131$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None					504.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{11}+\cdots\)
3528.3.d.e	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					504.3.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}-\beta _{3})q^{5}-\beta _{7}q^{11}+(-3-\beta _{1}+\cdots)q^{13}+\cdots\)
3528.3.d.f	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					504.3.cu.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+(\beta _{1}-\beta _{3}+2\beta _{7})q^{11}+(-2+\cdots)q^{13}+\cdots\)
3528.3.d.g	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					504.3.cu.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{6})q^{5}+(-\beta _{3}-\beta _{6})q^{11}+(-2+\cdots)q^{13}+\cdots\)
3528.3.d.h	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\Q(i, \sqrt{2}, \sqrt{35})\)	None		✓			3528.3.d.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(-4\beta _{2}-\beta _{5})q^{11}+\cdots\)
3528.3.d.i	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	8.0.\(\cdots\).20	None		✓			3528.3.d.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{4}q^{11}+(-\beta _{2}+\beta _{6})q^{13}+\cdots\)
3528.3.d.j	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					504.3.cu.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{6})q^{5}+(\beta _{3}+\beta _{6})q^{11}+(2-\beta _{2}+\cdots)q^{13}+\cdots\)
3528.3.d.k	$3528$	$3$	3528.d	3.b	$2$	$8$	$8$	$96.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					504.3.cu.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+(-\beta _{1}+\beta _{3}-2\beta _{7})q^{11}+\cdots\)
3528.3.d.l	$3528$	$3$	3528.d	3.b	$2$	$12$	$12$	$96.131$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		3528.3.d.l	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-\beta _{5}+\beta _{10})q^{11}+\beta _{9}q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3528, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)