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

• Label: 315.10.bo
• Level: $315$
• Weight: $10$
• Character orbit: 315.bo
• Rep. character: $\chi_{315}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $856$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

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

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

Trace form

856 * q + 108546 * q^4 - 2 * q^5 - 3528 * q^6 + 16048 * q^9 + 1022 * q^10 - 30828 * q^11 - 65762 * q^14 - 335471 * q^15 - 27263998 * q^16 - 4 * q^19 - 524802 * q^20 - 405098 * q^21 - 659004 * q^24 - 2 * q^25 - 10968452 * q^26 + 1558006 * q^29 - 3543784 * q^30 + 2 * q^31 - 1028 * q^34 - 670041 * q^35 + 53925588 * q^36 + 6691558 * q^39 + 4952776 * q^40 - 91540258 * q^41 - 16831492 * q^44 - 66143673 * q^45 + 6431068 * q^46 + 62143090 * q^49 + 78147754 * q^50 + 168208814 * q^51 + 58347240 * q^54 - 42273150 * q^55 + 18050862 * q^56 + 581633330 * q^59 + 72169464 * q^60 + 12227816 * q^61 - 13422819344 * q^64 + 239458807 * q^65 + 1107759658 * q^66 + 558253990 * q^69 + 69304146 * q^70 - 218822280 * q^71 - 472417804 * q^74 + 843272601 * q^75 + 526332 * q^76 - 144056446 * q^79 + 221960273 * q^80 + 193322504 * q^81 - 5429368954 * q^84 - 1953127 * q^85 + 3433930328 * q^86 + 3494945758 * q^89 + 5089914185 * q^90 - 161414436 * q^91 + 757691074 * q^94 + 165981203 * q^95 + 1196502834 * q^96 - 1989028650 * 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.