Space of modular forms of level 105, weight 8, and Character 105.j

• Label: 105.8.j
• Level: $105$
• Weight: $8$
• Character orbit: 105.j
• Rep. character: $\chi_{105}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $168$
• Sturm bound: $128$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(105, [\chi])\).

	Total	New	Old
Modular forms	232	168	64
Cusp forms	216	168	48
Eisenstein series	16	0	16

Trace form

168 * q - 52 * q^3 + 7184 * q^10 + 13312 * q^12 - 33704 * q^13 - 49936 * q^15 - 648712 * q^16 + 161980 * q^18 - 56252 * q^21 - 231184 * q^22 + 419744 * q^25 + 489008 * q^27 - 434980 * q^30 + 389760 * q^31 + 1173004 * q^33 + 928672 * q^36 + 1435808 * q^37 + 1095184 * q^40 - 1159340 * q^42 - 598600 * q^43 - 1583980 * q^45 - 3166288 * q^46 + 2129608 * q^48 + 6909340 * q^51 + 7074480 * q^52 - 1175480 * q^55 - 6748652 * q^57 - 1807640 * q^58 - 8227288 * q^60 - 4559776 * q^61 + 1232056 * q^63 + 35216288 * q^66 + 27094008 * q^67 + 3973312 * q^70 - 59658056 * q^72 + 4727936 * q^73 + 6379860 * q^75 - 33774976 * q^76 + 18589020 * q^78 + 45905524 * q^81 + 9343120 * q^82 + 49917864 * q^85 - 71754092 * q^87 - 106873512 * q^88 - 69327024 * q^90 - 16949688 * q^91 + 97428692 * q^93 + 70369248 * q^96 + 92039448 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)