Space of modular forms of level 128, weight 10, and Character 128.g

• Label: 128.10.g
• Level: $128$
• Weight: $10$
• Character orbit: 128.g
• Rep. character: $\chi_{128}(17,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $140$
• Sturm bound: $160$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(128, [\chi])\).

	Total	New	Old
Modular forms	592	148	444
Cusp forms	560	140	420
Eisenstein series	32	8	24

Trace form

140 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 + 3465980 * q^23 - 4 * q^25 + 12650092 * q^27 - 4 * q^29 - 22164496 * q^31 - 8 * q^33 + 38240620 * q^35 - 4 * q^37 - 72274196 * q^39 - 4 * q^41 + 38062460 * q^43 + 78728 * q^45 - 180107384 * q^51 + 149815692 * q^53 + 140108836 * q^55 - 4 * q^57 - 288075228 * q^59 + 180242204 * q^61 + 630118448 * q^63 - 8 * q^65 - 503547476 * q^67 - 764720356 * q^69 - 238101468 * q^71 - 4 * q^73 + 1146770576 * q^75 - 412088436 * q^77 - 2478583716 * q^83 + 7812496 * q^85 + 2350951628 * q^87 - 4 * q^89 + 1091566804 * q^91 - 78736 * q^93 - 5212839992 * q^95 - 8 * q^97 + 1556903760 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(128, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)