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

• Label: 112.2.w
• Level: $112$
• Weight: $2$
• Character orbit: 112.w
• Rep. character: $\chi_{112}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

56 * q - 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 - 20 * q^8 + 4 * q^10 - 6 * q^11 - 2 * q^12 - 8 * q^13 - 24 * q^14 - 16 * q^15 + 8 * q^16 - 4 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 - 10 * q^21 - 36 * q^22 + 18 * q^24 - 2 * q^26 - 20 * q^27 - 14 * q^28 + 8 * q^29 + 14 * q^30 + 20 * q^31 + 8 * q^32 - 4 * q^33 - 32 * q^34 - 2 * q^35 - 64 * q^36 - 10 * q^37 + 18 * q^38 + 50 * q^40 + 30 * q^42 - 16 * q^43 - 14 * q^44 - 28 * q^45 - 44 * q^47 + 40 * q^48 - 8 * q^49 + 24 * q^50 + 30 * q^51 + 4 * q^52 + 6 * q^53 + 82 * q^54 + 72 * q^56 - 14 * q^58 - 18 * q^59 + 22 * q^60 - 2 * q^61 + 28 * q^62 - 36 * q^63 + 80 * q^64 - 4 * q^65 + 2 * q^66 + 30 * q^67 + 24 * q^68 - 20 * q^69 + 76 * q^70 - 24 * q^72 - 38 * q^74 - 24 * q^75 - 68 * q^76 - 18 * q^77 + 132 * q^78 - 4 * q^79 - 52 * q^80 - 8 * q^81 - 18 * q^82 + 32 * q^83 + 68 * q^84 + 12 * q^85 - 44 * q^86 - 34 * q^88 - 20 * q^90 + 32 * q^91 + 68 * q^92 + 10 * q^93 - 54 * q^94 + 20 * q^95 - 128 * q^96 - 16 * q^97 - 28 * q^98 + 8 * 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.w.a	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	\(\Q(\zeta_{12})\)	None		✓			112.2.w.a	$2$	$0$	\(-2\)	\(-4\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
112.2.w.b	$112$	$2$	112.w	112.w	$12$	$4$	$1$	$0.894$	\(\Q(\zeta_{12})\)	None		✓			112.2.w.a	$2$	$0$	\(4\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
112.2.w.c	$112$	$2$	112.w	112.w	$12$	$48$	$12$	$0.894$		None		✓	✓		112.2.w.c	$4$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$