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

• Label: 208.10.l
• Level: $208$
• Weight: $10$
• Character orbit: 208.l
• Rep. character: $\chi_{208}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $500$
• Sturm bound: $280$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	508	508	0
Cusp forms	500	500	0
Eisenstein series	8	8	0

Trace form

500 * q - 2 * q^2 - 4 * q^3 + 3212 * q^6 - 4 * q^7 - 9080 * q^8 - 9400 * q^10 - 2 * q^13 - 221108 * q^14 + 78732 * q^15 - 4 * q^16 - 816514 * q^18 + 2287896 * q^20 - 78736 * q^21 + 758804 * q^22 - 7212972 * q^24 - 189062500 * q^25 - 11223754 * q^26 + 78728 * q^27 - 2580956 * q^28 - 4 * q^29 + 7812500 * q^30 - 26718732 * q^32 - 4 * q^33 + 9414640 * q^34 - 4 * q^35 - 26902908 * q^36 - 4 * q^37 + 62946568 * q^38 - 4 * q^39 - 77748844 * q^40 - 61518584 * q^42 + 53912304 * q^43 - 42934300 * q^44 + 7891228 * q^45 + 207804192 * q^46 + 6632656 * q^48 - 45774870 * q^50 + 16474120 * q^52 - 4 * q^53 + 261400220 * q^54 - 140108840 * q^55 + 119174900 * q^56 + 78732 * q^57 - 69972876 * q^58 + 482505724 * q^60 - 4 * q^61 - 78732 * q^63 + 840381252 * q^64 - 4 * q^65 - 472904304 * q^66 + 252130560 * q^68 - 448888992 * q^70 - 238101476 * q^71 + 1755585580 * q^72 + 241709752 * q^73 + 11273076 * q^74 - 569479036 * q^75 + 559232160 * q^76 + 161414428 * q^77 + 320708868 * q^78 + 472263424 * q^80 - 20145865436 * q^81 + 1341138856 * q^82 + 1454834068 * q^84 + 7812496 * q^85 + 277768416 * q^86 - 8 * q^87 + 536870912 * q^88 - 183385928 * q^89 + 7810452 * q^90 - 766546972 * q^91 + 741709848 * q^92 - 2143854376 * q^93 - 4836688796 * q^94 + 15625000 * q^95 - 6733472028 * q^96 - 4 * q^97 - 2447772398 * q^98 - 7221804 * 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.