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

• Label: 105.8.x
• Level: $105$
• Weight: $8$
• Character orbit: 105.x
• Rep. character: $\chi_{105}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $432$
• Sturm bound: $128$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	105.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(128\)

Dimensions

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

	Total	New	Old
Modular forms	464	464	0
Cusp forms	432	432	0
Eisenstein series	32	32	0

Trace form

432 * q - 2 * q^3 - 1872 * q^6 - 1356 * q^7 + 412 * q^10 - 8494 * q^12 - 16 * q^13 - 25196 * q^15 + 786424 * q^16 + 51134 * q^18 + 66332 * q^21 - 118352 * q^22 + 131764 * q^25 - 387032 * q^27 + 232536 * q^28 + 22420 * q^30 + 28200 * q^31 - 304420 * q^33 - 1297936 * q^36 - 164588 * q^37 - 1223056 * q^40 - 1549870 * q^42 - 2196080 * q^43 + 247000 * q^45 + 1204024 * q^46 + 2183204 * q^48 + 1146680 * q^51 + 5974788 * q^52 + 5073560 * q^55 - 2122552 * q^57 - 6225292 * q^58 + 2570170 * q^60 + 3821992 * q^61 - 8773084 * q^63 + 18955012 * q^66 - 3173172 * q^67 - 36016120 * q^70 - 25415854 * q^72 - 15695516 * q^73 - 10184154 * q^75 + 24716224 * q^76 + 32491848 * q^78 - 15278596 * q^81 + 31494728 * q^82 + 4235016 * q^85 - 22116742 * q^87 + 13232484 * q^88 + 18342996 * q^90 + 41132520 * q^91 + 8055124 * q^93 + 17195904 * q^96 + 171576 * 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.