Space of modular forms of level 105, weight 10, and Character 105.m

• Label: 105.10.m
• Level: $105$
• Weight: $10$
• Character orbit: 105.m
• Rep. character: $\chi_{105}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Sturm bound: $160$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(105, [\chi])\).

	Total	New	Old
Modular forms	296	144	152
Cusp forms	280	144	136
Eisenstein series	16	0	16

Trace form

144 * q + 2132 * q^7 - 2856 * q^8 + 227696 * q^11 - 77112 * q^15 - 7288352 * q^16 - 1630368 * q^21 + 4172544 * q^22 + 6014480 * q^23 - 2808520 * q^25 - 19690676 * q^28 - 3742848 * q^30 - 1462272 * q^32 + 47227432 * q^35 - 241864704 * q^36 - 9288408 * q^37 + 21222324 * q^42 + 105708864 * q^43 - 237615344 * q^46 - 362674872 * q^50 + 36269856 * q^51 - 225176256 * q^53 - 303191664 * q^56 - 55831032 * q^57 - 210743368 * q^58 + 485420040 * q^60 - 13988052 * q^63 - 838605200 * q^65 - 295413232 * q^67 + 1458894900 * q^70 - 231646544 * q^71 - 18738216 * q^72 - 921570384 * q^77 + 1361401992 * q^78 - 6198727824 * q^81 - 6191024072 * q^85 + 1095410416 * q^86 - 3373276144 * q^88 + 1047639648 * q^91 + 9749415080 * q^92 - 1807684776 * q^93 + 4105893888 * q^95 - 8832771216 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)