Space of modular forms of level 2106, weight 2, and Character 2106.e

• Label: 2106.2.e
• Level: $2106$
• Weight: $2$
• Character orbit: 2106.e
• Rep. character: $\chi_{2106}(703,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $36$
• Sturm bound: $756$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 36 \)
Sturm bound:			\(756\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2106, [\chi])\).

	Total	New	Old
Modular forms	804	96	708
Cusp forms	708	96	612
Eisenstein series	96	0	96

Trace form

96 * q - 48 * q^4 - 48 * q^16 - 24 * q^19 + 12 * q^22 - 24 * q^25 + 24 * q^31 + 12 * q^34 - 48 * q^37 + 12 * q^43 - 48 * q^46 - 24 * q^49 + 72 * q^55 - 60 * q^58 + 24 * q^61 + 96 * q^64 + 36 * q^67 - 36 * q^70 - 24 * q^73 + 12 * q^76 - 60 * q^79 - 24 * q^82 + 12 * q^88 + 24 * q^94 + 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2106, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2106.2.e.a	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
2106.2.e.b	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					26.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
2106.2.e.c	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
2106.2.e.d	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.b	$2$	$1$	\(-1\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
2106.2.e.e	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					234.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
2106.2.e.f	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.d	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
2106.2.e.g	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None		✓			2106.2.a.a	$2$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
2106.2.e.h	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					26.2.a.b	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.e.i	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.e	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
2106.2.e.j	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					78.2.a.a	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
2106.2.e.k	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.g	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
2106.2.e.l	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None		✓			2106.2.a.c	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
2106.2.e.m	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.f	$2$	$0$	\(-1\)	\(0\)	\(2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
2106.2.e.n	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.h	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots\)
2106.2.e.o	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.h	$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.e.p	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.g	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
2106.2.e.q	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					78.2.a.a	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
2106.2.e.r	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None		✓			2106.2.a.c	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.e.s	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.f	$2$	$0$	\(1\)	\(0\)	\(-2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
2106.2.e.t	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					26.2.a.b	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.e.u	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.e	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+\cdots\)
2106.2.e.v	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None		✓			2106.2.a.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
2106.2.e.w	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.d	$2$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}+\cdots\)
2106.2.e.x	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.c	$2$	$0$	\(1\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
2106.2.e.y	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.b	$2$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.e.z	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					234.2.a.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
2106.2.e.ba	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					26.2.a.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
2106.2.e.bb	$2106$	$2$	2106.e	9.c	$3$	$2$	$1$	$16.816$	\(\Q(\sqrt{-3}) \)	None					702.2.a.a	$2$	$0$	\(1\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
2106.2.e.bc	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2106.2.a.g	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots\)
2106.2.e.bd	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\zeta_{12})\)	None		✓			2106.2.a.k	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}-\beta_1 q^{4}+(-\beta_{2}+\beta_1)q^{5}+\cdots\)
2106.2.e.be	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\zeta_{12})\)	None		✓			2106.2.a.j	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_1-1)q^{2}-\beta_1 q^{4}+(-\beta_{2}+\beta_1)q^{5}+\cdots\)
2106.2.e.bf	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\zeta_{12})\)	None		✓			2106.2.a.k	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_1+1)q^{2}-\beta_1 q^{4}+(\beta_{2}-\beta_1)q^{5}+\cdots\)
2106.2.e.bg	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\zeta_{12})\)	None		✓			2106.2.a.j	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_1+1)q^{2}-\beta_1 q^{4}+(\beta_{2}-\beta_1)q^{5}+\cdots\)
2106.2.e.bh	$2106$	$2$	2106.e	9.c	$3$	$4$	$2$	$16.816$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2106.2.a.g	$2$	$0$	\(2\)	\(0\)	\(4\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(2-2\beta _{1}+\cdots)q^{5}+\cdots\)
2106.2.e.bi	$2106$	$2$	2106.e	9.c	$3$	$8$	$4$	$16.816$	8.0.49787136.1	None		✓			2106.2.a.s	$2$	$0$	\(-4\)	\(0\)	\(-2\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}-\beta _{3}q^{7}+\cdots\)
2106.2.e.bj	$2106$	$2$	2106.e	9.c	$3$	$8$	$4$	$16.816$	8.0.49787136.1	None		✓			2106.2.a.s	$2$	$0$	\(4\)	\(0\)	\(2\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2106, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2106, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(702, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1053, [\chi])\)\(^{\oplus 2}\)