Space of modular forms of level 128, weight 12, and Character 128.g

• Label: 128.12.g
• Level: $128$
• Weight: $12$
• Character orbit: 128.g
• Rep. character: $\chi_{128}(17,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $172$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(128, [\chi])\).

	Total	New	Old
Modular forms	720	180	540
Cusp forms	688	172	516
Eisenstein series	32	8	24

Trace form

172 * 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 - 13479492 * q^23 - 4 * q^25 - 133635188 * q^27 - 4 * q^29 + 687099632 * q^31 - 8 * q^33 - 1064775860 * q^35 - 4 * q^37 + 579959980 * q^39 - 4 * q^41 + 2884696668 * q^43 + 708584 * q^45 + 223733992 * q^51 + 4201216108 * q^53 - 19122805468 * q^55 - 4 * q^57 + 22992780452 * q^59 - 4301654052 * q^61 - 39697461712 * q^63 - 8 * q^65 + 50706890124 * q^67 + 32386830044 * q^69 - 43677902044 * q^71 - 4 * q^73 + 56217569072 * q^75 + 53333048044 * q^77 - 11370505476 * q^83 + 195312496 * q^85 + 50128110092 * q^87 - 4 * q^89 - 209413389548 * q^91 - 708592 * q^93 + 495219800008 * q^95 - 8 * q^97 - 378702509904 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

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

Decomposition of \(S_{12}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(128, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)