Space of modular forms of level 315, weight 5, and Character 315.ch

• Label: 315.5.ch
• Level: $315$
• Weight: $5$
• Character orbit: 315.ch
• Rep. character: $\chi_{315}(67,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $752$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	315.ch (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

752 * q + 2 * q^2 - 2 * q^3 - 4 * q^5 - 144 * q^6 - 2 * q^7 + 48 * q^8 - 4 * q^10 + 304 * q^11 - 262 * q^12 - 4 * q^13 + 166 * q^15 + 22532 * q^16 - 454 * q^17 + 1214 * q^18 + 1020 * q^20 + 1112 * q^21 - 68 * q^22 + 956 * q^23 - 4 * q^25 - 8 * q^26 - 788 * q^27 + 536 * q^28 - 1004 * q^30 + 4 * q^31 + 2918 * q^32 - 1300 * q^33 - 6092 * q^35 + 368 * q^36 - 4 * q^37 - 132 * q^38 - 2052 * q^40 + 2968 * q^41 + 3098 * q^42 - 4 * q^43 + 12424 * q^45 - 2120 * q^46 + 2 * q^47 - 9994 * q^48 + 692 * q^50 + 11828 * q^51 - 1924 * q^52 + 4496 * q^53 - 2516 * q^55 - 1488 * q^56 + 19928 * q^57 - 9732 * q^58 + 6586 * q^60 + 5572 * q^61 + 5680 * q^62 - 19966 * q^63 + 13538 * q^65 + 59884 * q^66 + 2 * q^67 - 30980 * q^68 + 4998 * q^70 + 736 * q^71 - 1630 * q^72 - 4 * q^73 - 20226 * q^75 - 1032 * q^76 - 35050 * q^77 + 25242 * q^78 - 3016 * q^80 + 17480 * q^81 + 28 * q^82 + 21416 * q^83 - 4 * q^85 - 78992 * q^86 + 4700 * q^87 - 18564 * q^88 - 48012 * q^90 - 16 * q^91 - 10468 * q^92 + 712 * q^93 - 28890 * q^95 - 75684 * q^96 - 4 * q^97 - 32556 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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