Space of modular forms of level 416, weight 4, and Character 416.ca

• Label: 416.4.ca
• Level: $416$
• Weight: $4$
• Character orbit: 416.ca
• Rep. character: $\chi_{416}(29,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $1328$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	416.ca (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(416, [\chi])\).

	Total	New	Old
Modular forms	1360	1360	0
Cusp forms	1328	1328	0
Eisenstein series	32	32	0

Trace form

1328 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 4 * q^6 - 4 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 112 * q^12 - 8 * q^13 + 400 * q^14 - 4 * q^16 - 16 * q^18 - 4 * q^19 + 76 * q^20 - 16 * q^21 - 436 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 + 32 * q^26 + 512 * q^27 + 376 * q^28 - 4 * q^29 - 68 * q^30 - 32 * q^31 + 616 * q^32 - 8 * q^33 - 1080 * q^34 - 4 * q^35 + 1016 * q^36 - 4 * q^37 + 424 * q^38 + 1192 * q^39 + 1624 * q^40 - 4 * q^41 + 676 * q^42 - 4 * q^43 - 16 * q^44 - 220 * q^45 + 2876 * q^46 - 2448 * q^48 + 4260 * q^50 - 232 * q^51 - 80 * q^52 - 16 * q^53 - 4 * q^54 + 284 * q^55 - 1004 * q^56 - 16 * q^57 - 2380 * q^58 + 1372 * q^59 - 5424 * q^60 - 4 * q^61 + 456 * q^62 - 8 * q^63 - 16 * q^64 - 16 * q^65 + 13232 * q^66 - 4 * q^67 - 1548 * q^68 - 4 * q^69 + 3224 * q^70 - 452 * q^71 - 328 * q^72 - 16 * q^73 - 4 * q^74 + 2704 * q^75 + 4284 * q^76 - 16 * q^77 - 5652 * q^78 + 9276 * q^80 + 6956 * q^82 - 16 * q^83 + 8964 * q^84 + 496 * q^85 + 3392 * q^86 - 4 * q^87 + 1556 * q^88 - 4 * q^89 - 11104 * q^90 + 3592 * q^91 + 11072 * q^92 - 112 * q^93 + 4708 * q^94 + 12152 * q^95 - 22688 * q^96 - 8 * q^97 - 68 * q^98 - 21048 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(416, [\chi])\) into newform subspaces

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