Space of modular forms of level 208, weight 10, and Character 208.bf

• Label: 208.10.bf
• Level: $208$
• Weight: $10$
• Character orbit: 208.bf
• Rep. character: $\chi_{208}(11,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1000$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	208.bf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(208, [\chi])\).

	Total	New	Old
Modular forms	1016	1016	0
Cusp forms	1000	1000	0
Eisenstein series	16	16	0

Trace form

1000 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 3218 * q^6 - 8 * q^7 + 9074 * q^8 + 12466 * q^10 - 6 * q^11 - 4 * q^13 + 221096 * q^14 + 157464 * q^15 - 1611626 * q^16 - 12 * q^17 - 1754198 * q^18 - 6 * q^19 + 1999962 * q^20 + 78724 * q^21 - 758810 * q^22 - 12 * q^23 - 2601564 * q^24 - 378125000 * q^25 + 11223748 * q^26 - 78740 * q^27 - 13762660 * q^28 - 2 * q^29 + 3906244 * q^30 - 11772504 * q^32 - 8 * q^33 - 5373022 * q^34 + 11718748 * q^35 - 90515520 * q^36 - 2 * q^37 + 14227652 * q^38 - 8 * q^39 + 77748832 * q^40 + 61515506 * q^42 - 53912310 * q^43 + 5077744 * q^44 + 3827516 * q^45 - 207804198 * q^46 - 6632662 * q^48 - 12 * q^49 + 57490542 * q^50 - 16474126 * q^52 - 8 * q^53 + 443921254 * q^54 + 140108828 * q^55 + 59587444 * q^56 - 78732 * q^57 + 747883902 * q^58 + 432112842 * q^59 + 257343080 * q^60 - 2 * q^61 + 304833792 * q^62 - 157464 * q^63 - 762652392 * q^64 - 8 * q^65 - 945808608 * q^66 - 6 * q^67 - 252130566 * q^68 - 6 * q^69 - 941211312 * q^70 + 238101464 * q^71 - 1755585586 * q^72 - 241709752 * q^73 - 1243129494 * q^74 + 581079682 * q^75 + 1393938804 * q^76 - 161414428 * q^77 + 6117349536 * q^78 + 1238625320 * q^80 + 20145865424 * q^81 + 2888781548 * q^82 - 5962542988 * q^84 + 3906248 * q^85 - 2765158836 * q^86 - 4 * q^87 - 1125869720 * q^88 + 183385928 * q^89 + 15627048 * q^90 - 3412565786 * q^91 + 1480273968 * q^92 + 2143972468 * q^93 - 3151931968 * q^94 + 7812500 * q^95 + 1973215764 * q^96 - 8 * q^97 - 11864882632 * q^98 - 4663253280 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(208, [\chi])\) into newform subspaces

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