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

• Label: 208.10.i
• Level: $208$
• Weight: $10$
• Character orbit: 208.i
• Rep. character: $\chi_{208}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $124$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(280\)

Dimensions

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

	Total	New	Old
Modular forms	516	128	388
Cusp forms	492	124	368
Eisenstein series	24	4	20

Trace form

124 * q + 163 * q^3 + 714 * q^5 - 1025 * q^7 - 393661 * q^9 + q^11 + 43077 * q^13 + 19684 * q^15 + 50998 * q^17 - 670139 * q^19 + 39362 * q^21 - 1679045 * q^23 + 46173378 * q^25 - 2217374 * q^27 - 531720 * q^29 - 15617516 * q^31 + 39365 * q^33 + 19960626 * q^35 + 801404 * q^37 - 11734093 * q^39 - 2688754 * q^41 + 15398935 * q^43 - 13690755 * q^45 + 108755692 * q^47 - 346229561 * q^49 - 45624770 * q^51 - 13473262 * q^53 - 17901494 * q^55 + 95819938 * q^57 - 40839657 * q^59 + 145168504 * q^61 - 107613874 * q^63 + 166779363 * q^65 - 146618477 * q^67 + 85149325 * q^69 - 167990811 * q^71 - 80287266 * q^73 + 156295791 * q^75 + 910980290 * q^77 + 857119296 * q^79 - 2094496850 * q^81 + 397761584 * q^83 + 144296185 * q^85 - 2246644631 * q^87 + 496004705 * q^89 + 2272282667 * q^91 + 1206332476 * q^93 - 2289256212 * q^95 - 941719279 * q^97 - 4366285948 * 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.

Decomposition of \(S_{10}^{\mathrm{old}}(208, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(208, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)