Space of modular forms of level 112, weight 2, and Character 112.m

• Label: 112.2.m
• Level: $112$
• Weight: $2$
• Character orbit: 112.m
• Rep. character: $\chi_{112}(29,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

	Total	New	Old
Modular forms	36	24	12
Cusp forms	28	24	4
Eisenstein series	8	0	8

Trace form

24 * q - 2 * q^4 - 12 * q^6 + 8 * q^10 - 4 * q^11 + 4 * q^12 - 2 * q^14 - 16 * q^15 + 2 * q^16 + 10 * q^18 - 16 * q^19 - 28 * q^20 + 18 * q^22 - 24 * q^24 - 12 * q^26 + 24 * q^27 - 8 * q^29 - 24 * q^30 + 12 * q^34 - 8 * q^37 + 20 * q^40 - 28 * q^43 - 26 * q^44 + 52 * q^48 - 24 * q^49 + 18 * q^50 + 16 * q^51 + 16 * q^52 + 8 * q^53 + 32 * q^54 + 14 * q^56 + 26 * q^58 - 24 * q^59 + 32 * q^60 + 32 * q^61 + 36 * q^62 + 20 * q^63 - 50 * q^64 - 16 * q^65 - 28 * q^66 + 20 * q^67 + 32 * q^69 + 24 * q^70 + 58 * q^72 - 34 * q^74 - 24 * q^75 + 32 * q^76 + 8 * q^77 - 64 * q^78 - 8 * q^79 + 12 * q^80 - 24 * q^81 - 36 * q^82 - 40 * q^83 - 32 * q^85 + 62 * q^86 - 54 * q^88 - 56 * q^90 + 52 * q^92 - 48 * q^93 + 44 * q^94 + 64 * q^95 - 8 * q^96 + 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
112.2.m.a	$112$	$2$	112.m	16.e	$4$	$2$	$1$	$0.894$	\(\Q(\sqrt{-1}) \)	None		✓			112.2.m.a	$2$	$1$	\(-2\)	\(-4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}+(2 i-2)q^{3}-2 i q^{4}+\cdots\)
112.2.m.b	$112$	$2$	112.m	16.e	$4$	$2$	$1$	$0.894$	\(\Q(\sqrt{-1}) \)	None		✓			112.2.m.b	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}-2 i q^{4}+(2 i+2)q^{5}+\cdots\)
112.2.m.c	$112$	$2$	112.m	16.e	$4$	$8$	$4$	$0.894$	8.0.214798336.3	None		✓			112.2.m.c	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
112.2.m.d	$112$	$2$	112.m	16.e	$4$	$12$	$6$	$0.894$	12.0.\(\cdots\).1	None		✓	✓		112.2.m.d	$2$	$0$	\(2\)	\(4\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{10})q^{3}+\beta _{1}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(112, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)