Space of modular forms of level 234, weight 8, and Character 234.t

• Label: 234.8.t
• Level: $234$
• Weight: $8$
• Character orbit: 234.t
• Rep. character: $\chi_{234}(25,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $196$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(234, [\chi])\).

	Total	New	Old
Modular forms	596	196	400
Cusp forms	580	196	384
Eisenstein series	16	0	16

Trace form

196 * q + 6272 * q^4 + 4592 * q^9 - 3694 * q^13 - 21952 * q^14 - 401408 * q^16 - 78608 * q^17 + 2296 * q^23 + 1531250 * q^25 + 52928 * q^26 - 344934 * q^27 + 156296 * q^29 - 124736 * q^30 - 206132 * q^35 + 146944 * q^36 + 1347840 * q^38 - 220064 * q^39 - 1504240 * q^42 - 48052 * q^43 + 10944286 * q^49 + 6222898 * q^51 + 236416 * q^52 + 6542520 * q^53 + 1404928 * q^56 - 5738852 * q^61 - 6253024 * q^62 - 51380224 * q^64 - 9350684 * q^65 - 5105472 * q^66 - 2515456 * q^68 + 5669500 * q^69 - 1023104 * q^74 - 2512384 * q^75 + 12948312 * q^77 + 13117904 * q^78 - 5041172 * q^79 + 7210520 * q^81 + 19031424 * q^82 - 23197564 * q^87 - 48118064 * q^90 + 2333664 * q^91 - 146944 * q^92 + 38104128 * q^95

Decomposition of \(S_{8}^{\mathrm{new}}(234, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(234, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)