Space of modular forms of level 2112, weight 2, and Character 2112.m

• Label: 2112.2.m
• Level: $2112$
• Weight: $2$
• Character orbit: 2112.m
• Rep. character: $\chi_{2112}(1121,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $13$
• Sturm bound: $768$
• Trace bound: $39$

Defining parameters

Level:	\( N \)	\(=\)	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2112.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(768\)
Trace bound:			\(39\)
Distinguishing \(T_p\):			\(5\), \(17\), \(167\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

\( 96 q + 96 q^{25} + 24 q^{33} - 96 q^{49} + 48 q^{81} - 96 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2112.2.m.a	$2112$	$2$	2112.m	264.m	$2$	$4$	$4$	$16.864$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		✓			2112.2.m.a	$8$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}-3q^{5}+(3+\beta _{3})q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
2112.2.m.b	$2112$	$2$	2112.m	264.m	$2$	$4$	$4$	$16.864$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		✓			2112.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_1 q^{3}+(-\beta_{3}+1)q^{9}+(-2\beta_{2}+\beta_1)q^{11}+\cdots\)
2112.2.m.c	$2112$	$2$	2112.m	264.m	$2$	$4$	$4$	$16.864$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		✓			2112.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_1 q^{3}+(-\beta_{3}+1)q^{9}+(-\beta_{2}+2\beta_1)q^{11}+\cdots\)
2112.2.m.d	$2112$	$2$	2112.m	264.m	$2$	$4$	$4$	$16.864$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		✓			2112.2.m.a	$8$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+3q^{5}+(2-\beta _{3})q^{9}+\cdots\)
2112.2.m.e	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.e	$8$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{3}-2 q^{5}-\beta_1 q^{7}+3 q^{9}+\cdots\)
2112.2.m.f	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	8.0.303595776.1	\(\Q(\sqrt{-11}) \)		✓			2112.2.m.f	$8$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+(-2+\beta _{2}+\cdots)q^{5}+\cdots\)
2112.2.m.g	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.g	$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta_{3}+\beta_1)q^{3}-q^{5}+(\beta_{6}-\beta_{5})q^{7}+\cdots\)
2112.2.m.h	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{6}+\beta_1)q^{3}+\beta_{5} q^{5}-3\beta_{3} q^{7}+\cdots\)
2112.2.m.i	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{6}+\beta_1)q^{3}+\beta_{5} q^{5}-3\beta_{3} q^{7}+\cdots\)
2112.2.m.j	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.g	$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta_{3}+\beta_1)q^{3}+q^{5}+(\beta_{6}-\beta_{5})q^{7}+\cdots\)
2112.2.m.k	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	8.0.303595776.1	\(\Q(\sqrt{-11}) \)		✓			2112.2.m.f	$8$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{4}q^{3}+(2-\beta _{2}-\beta _{6})q^{5}+(-1-\beta _{6}+\cdots)q^{9}+\cdots\)
2112.2.m.l	$2112$	$2$	2112.m	264.m	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{24})\)	None		✓			2112.2.m.e	$8$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{3}+2 q^{5}+\beta_1 q^{7}+3 q^{9}+\cdots\)
2112.2.m.m	$2112$	$2$	2112.m	264.m	$2$	$16$	$16$	$16.864$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	\(\Q(\sqrt{-66}) \)		✓	✓		2112.2.m.m	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{8}q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)