Space of modular forms of level 315, weight 10, and Character 315.k

• Label: 315.10.k
• Level: $315$
• Weight: $10$
• Character orbit: 315.k
• Rep. character: $\chi_{315}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $576$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	872	576	296
Cusp forms	856	576	280
Eisenstein series	16	0	16

Trace form

576 * q - 73728 * q^4 + 5000 * q^5 + 4544 * q^6 + 684 * q^7 + 16050 * q^9 + 30824 * q^11 - 110660 * q^12 + 64872 * q^13 + 641988 * q^14 - 132500 * q^15 - 18874368 * q^16 - 1336336 * q^17 - 2593836 * q^18 + 446760 * q^19 - 1920000 * q^20 + 232970 * q^21 - 3399144 * q^23 - 7793396 * q^24 + 225000000 * q^25 - 3674240 * q^26 - 704604 * q^27 + 700416 * q^28 + 1558010 * q^29 + 4760000 * q^30 - 7808760 * q^31 - 14252140 * q^32 - 6089272 * q^33 - 76113480 * q^36 - 6476904 * q^37 + 48637048 * q^38 - 6628696 * q^39 + 36618142 * q^41 - 6640332 * q^42 + 32070024 * q^43 + 23470402 * q^44 + 10353750 * q^45 - 6429024 * q^46 - 156501076 * q^47 + 261417836 * q^48 + 70747812 * q^49 + 106104524 * q^51 - 132857856 * q^52 + 65919960 * q^53 - 264363600 * q^54 + 757989678 * q^56 - 90501904 * q^57 + 24318500 * q^59 + 82893750 * q^60 + 150612066 * q^61 - 148967880 * q^62 - 522436168 * q^63 + 9663676416 * q^64 - 23080000 * q^65 - 1305374096 * q^66 - 278498556 * q^67 + 1376862116 * q^68 - 975974784 * q^69 + 156060000 * q^70 - 907948464 * q^71 - 2013802504 * q^72 + 690199776 * q^73 + 329924336 * q^74 + 457482240 * q^76 - 1405254992 * q^77 + 1666830376 * q^78 + 325811664 * q^79 - 1146880000 * q^80 - 1405909882 * q^81 - 3517291268 * q^83 + 971389344 * q^84 - 255015000 * q^85 + 561266732 * q^86 - 1180021612 * q^87 + 902292034 * q^89 - 902801250 * q^90 + 39409380 * q^91 + 3672596900 * q^92 - 1735640832 * q^93 + 757695168 * q^94 + 7898520610 * q^96 + 452087856 * q^97 + 3950188298 * q^98 + 3387188460 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)