Space of modular forms of level 936, weight 4, and Character 936.by

• Label: 936.4.by
• Level: $936$
• Weight: $4$
• Character orbit: 936.by
• Rep. character: $\chi_{936}(131,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $864$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	936.by (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(936, [\chi])\).

	Total	New	Old
Modular forms	1016	864	152
Cusp forms	1000	864	136
Eisenstein series	16	0	16

Trace form

864 * q - 110 * q^12 - 150 * q^14 - 546 * q^18 + 462 * q^20 - 514 * q^24 - 10800 * q^25 - 846 * q^30 + 1380 * q^32 + 464 * q^33 - 396 * q^34 + 480 * q^36 + 870 * q^38 - 180 * q^40 - 120 * q^41 - 788 * q^42 - 72 * q^46 + 20 * q^48 + 21168 * q^49 + 1400 * q^51 + 1928 * q^54 - 3948 * q^56 + 344 * q^57 - 1836 * q^60 + 1368 * q^64 - 2386 * q^66 + 4710 * q^68 + 2328 * q^72 + 6342 * q^74 + 6608 * q^75 + 1116 * q^76 - 910 * q^78 + 312 * q^81 - 7320 * q^83 + 654 * q^84 + 8340 * q^86 - 1044 * q^88 - 11406 * q^90 + 5472 * q^92 + 828 * q^94 + 7972 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(936, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(936, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)