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

• Label: 105.10.j
• Level: $105$
• Weight: $10$
• Character orbit: 105.j
• Rep. character: $\chi_{105}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Sturm bound: $160$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
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	216	80
Cusp forms	280	216	64
Eisenstein series	16	0	16

Trace form

216 * q + 296 * q^3 - 22896 * q^10 - 303104 * q^12 - 228528 * q^13 - 161296 * q^15 - 13787784 * q^16 - 1715300 * q^18 + 38416 * q^21 + 2198448 * q^22 - 8730936 * q^25 + 702704 * q^27 + 11065820 * q^30 - 13507200 * q^31 - 22344392 * q^33 + 49811104 * q^36 + 51561144 * q^37 - 208419696 * q^40 - 30300620 * q^42 + 152604720 * q^43 + 64388720 * q^45 - 57722256 * q^46 - 509511704 * q^48 + 8410120 * q^51 + 366755760 * q^52 - 248659920 * q^55 + 180725944 * q^57 + 4622760 * q^58 + 266375432 * q^60 + 180242208 * q^61 + 255831352 * q^63 + 124694816 * q^66 - 13240656 * q^67 + 307020672 * q^70 + 2319893272 * q^72 + 280516752 * q^73 - 409922400 * q^75 + 2354465088 * q^76 + 2726497980 * q^78 - 3128106272 * q^81 - 1526695920 * q^82 + 50424264 * q^85 + 4925988184 * q^87 + 5846236056 * q^88 + 1698526896 * q^90 + 1718693424 * q^91 + 1037423504 * q^93 + 2152629216 * q^96 - 2683573056 * q^97

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

\( S_{10}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)