Space of modular forms of level 588, weight 8, and Character 588.x

• Label: 588.8.x
• Level: $588$
• Weight: $8$
• Character orbit: 588.x
• Rep. character: $\chi_{588}(55,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $2352$
• Sturm bound: $896$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 196 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(588, [\chi])\).

	Total	New	Old
Modular forms	4728	2352	2376
Cusp forms	4680	2352	2328
Eisenstein series	48	0	48

Trace form

2352 * q - 2004 * q^8 - 285768 * q^9 - 4282 * q^14 + 63632 * q^16 - 13716 * q^21 + 94236 * q^22 - 348138 * q^24 + 6104512 * q^25 - 646300 * q^28 - 162864 * q^30 - 729140 * q^32 + 1004976 * q^34 + 1585060 * q^37 + 2455544 * q^40 - 330048 * q^42 - 5164280 * q^44 + 2769760 * q^46 - 782448 * q^49 - 22655076 * q^50 + 1370192 * q^53 + 1040614 * q^56 + 4653288 * q^57 - 2620756 * q^58 + 1934820 * q^60 + 1076012 * q^61 - 6148128 * q^64 - 166000 * q^65 - 5062630 * q^70 + 3652290 * q^72 + 8824244 * q^74 - 8633058 * q^76 - 9694928 * q^77 - 7371324 * q^78 - 208324872 * q^81 + 15621200 * q^82 - 11920176 * q^84 - 21231888 * q^85 - 16351144 * q^86 - 81061604 * q^88 - 4886602 * q^92 - 9661464 * q^93 + 112774242 * q^94 + 37089596 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)