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

• Label: 2106.2.b
• Level: $2106$
• Weight: $2$
• Character orbit: 2106.b
• Rep. character: $\chi_{2106}(649,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $756$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(756\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	402	56	346
Cusp forms	354	56	298
Eisenstein series	48	0	48

Trace form

\( 56 q - 56 q^{4} + O(q^{10}) \)

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.b.a	$2106$	$2$	2106.b	13.b	$2$	$6$	$6$	$16.816$	6.0.5089536.1	None		✓			2106.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{2}q^{7}+\cdots\)
2106.2.b.b	$2106$	$2$	2106.b	13.b	$2$	$6$	$6$	$16.816$	6.0.5089536.1	None		✓			2106.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{4}+(\beta _{4}+\beta _{5})q^{5}-\beta _{2}q^{7}+\cdots\)
2106.2.b.c	$2106$	$2$	2106.b	13.b	$2$	$14$	$14$	$16.816$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None					234.2.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}-q^{4}-\beta _{11}q^{5}+(\beta _{1}+\beta _{8}+\cdots)q^{7}+\cdots\)
2106.2.b.d	$2106$	$2$	2106.b	13.b	$2$	$14$	$14$	$16.816$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None					234.2.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}-q^{4}-\beta _{11}q^{5}+(-\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots\)
2106.2.b.e	$2106$	$2$	2106.b	13.b	$2$	$16$	$16$	$16.816$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		2106.2.b.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{5}-\beta _{9}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2106, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(702, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1053, [\chi])\)\(^{\oplus 2}\)