Space of modular forms of level 112, weight 8, and Character 112.v

• Label: 112.8.v
• Level: $112$
• Weight: $8$
• Character orbit: 112.v
• Rep. character: $\chi_{112}(3,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $440$
• Sturm bound: $128$

Defining parameters

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(112, [\chi])\).

	Total	New	Old
Modular forms	456	456	0
Cusp forms	440	440	0
Eisenstein series	16	16	0

Trace form

440 * q - 2 * q^2 - 6 * q^3 + 180 * q^4 - 6 * q^5 - 8 * q^7 - 2012 * q^8 - 19428 * q^10 + 1202 * q^11 - 6 * q^12 - 25940 * q^14 - 26392 * q^16 - 12 * q^17 - 72974 * q^18 - 6 * q^19 - 4378 * q^21 + 325692 * q^22 + 143412 * q^23 - 6 * q^24 - 6 * q^26 + 415770 * q^28 + 103368 * q^29 + 435234 * q^30 + 534228 * q^32 - 12 * q^33 + 251998 * q^35 + 1969216 * q^36 + 415574 * q^37 - 6 * q^38 - 4 * q^39 + 3275934 * q^40 + 1750490 * q^42 + 366176 * q^43 - 1825558 * q^44 + 13116 * q^45 - 464980 * q^46 - 8 * q^49 + 1903272 * q^50 - 1125970 * q^51 - 8459556 * q^52 - 907818 * q^53 - 13459530 * q^54 - 6835568 * q^56 - 1742902 * q^58 + 2753898 * q^59 - 1254618 * q^60 - 6 * q^61 + 21407664 * q^64 - 4 * q^65 - 16736202 * q^66 + 5564454 * q^67 - 15288816 * q^68 + 11369012 * q^70 - 24697424 * q^71 + 11692156 * q^72 - 526786 * q^74 + 468744 * q^75 + 1647082 * q^77 - 40414364 * q^78 + 23665836 * q^80 + 99910904 * q^81 - 36986754 * q^82 + 18348976 * q^84 - 312508 * q^85 - 468828 * q^86 - 12 * q^87 + 17337214 * q^88 + 4234736 * q^91 - 49954868 * q^92 + 8746 * q^93 + 22545390 * q^94 - 3501084 * q^96 - 9813912 * q^98 - 10363472 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.