Space of modular forms of level 8100, weight 2, and Character 8100.d

• Label: 8100.2.d
• Level: $8100$
• Weight: $2$
• Character orbit: 8100.d
• Rep. character: $\chi_{8100}(649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $19$
• Sturm bound: $3240$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8100.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(3240\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8100, [\chi])\).

	Total	New	Old
Modular forms	1728	72	1656
Cusp forms	1512	72	1440
Eisenstein series	216	0	216

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8100.2.d.a	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					324.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}-6q^{11}-5iq^{13}-3iq^{17}+\cdots\)
8100.2.d.b	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					1620.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}-3q^{11}-2iq^{13}-5q^{19}+\cdots\)
8100.2.d.c	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-3q^{11}-iq^{13}+6iq^{17}+\cdots\)
8100.2.d.d	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					1620.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-3q^{11}+2iq^{13}-3iq^{17}+\cdots\)
8100.2.d.e	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					180.2.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-4iq^{13}+6iq^{17}-2q^{19}+\cdots\)
8100.2.d.f	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					180.2.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-4iq^{13}-6iq^{17}-2q^{19}+\cdots\)
8100.2.d.g	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					1620.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}+3q^{11}-2iq^{13}-5q^{19}+\cdots\)
8100.2.d.h	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{11}-iq^{13}-6iq^{17}+\cdots\)
8100.2.d.i	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					1620.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{11}+2iq^{13}+3iq^{17}+\cdots\)
8100.2.d.j	$8100$	$2$	8100.d	5.b	$2$	$2$	$2$	$64.679$	\(\Q(\sqrt{-1}) \)	None					324.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}+6q^{11}-5iq^{13}+3iq^{17}+\cdots\)
8100.2.d.k	$8100$	$2$	8100.d	5.b	$2$	$4$	$4$	$64.679$	\(\Q(i, \sqrt{5})\)	None		✓			8100.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
8100.2.d.l	$8100$	$2$	8100.d	5.b	$2$	$4$	$4$	$64.679$	\(\Q(\zeta_{12})\)	None					1620.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{7}+\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots\)
8100.2.d.m	$8100$	$2$	8100.d	5.b	$2$	$4$	$4$	$64.679$	\(\Q(\zeta_{12})\)	None					1620.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}-2\zeta_{12}^{3}q^{13}+\cdots\)
8100.2.d.n	$8100$	$2$	8100.d	5.b	$2$	$4$	$4$	$64.679$	\(\Q(i, \sqrt{5})\)	None		✓			8100.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
8100.2.d.o	$8100$	$2$	8100.d	5.b	$2$	$6$	$6$	$64.679$	6.0.5089536.1	None					180.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{7}+\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots\)
8100.2.d.p	$8100$	$2$	8100.d	5.b	$2$	$6$	$6$	$64.679$	6.0.5089536.1	None					180.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{7}-\beta _{1}q^{11}+(-\beta _{3}-\beta _{5})q^{13}+\cdots\)
8100.2.d.q	$8100$	$2$	8100.d	5.b	$2$	$8$	$8$	$64.679$	8.0.4057180416.1	None					900.2.i.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{7}+(-1-\beta _{1})q^{11}-\beta _{2}q^{13}+\cdots\)
8100.2.d.r	$8100$	$2$	8100.d	5.b	$2$	$8$	$8$	$64.679$	8.0.49787136.1	None		✓			8100.2.a.w	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{7}-\beta _{5}q^{11}-\beta _{1}q^{13}+\beta _{6}q^{17}+\cdots\)
8100.2.d.s	$8100$	$2$	8100.d	5.b	$2$	$8$	$8$	$64.679$	8.0.4057180416.1	None					900.2.i.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{7}+(1+\beta _{1})q^{11}-\beta _{2}q^{13}+(2\beta _{3}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(8100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4050, [\chi])\)\(^{\oplus 2}\)