Space of modular forms of level 273, weight 4, and Character 273.bt

• Label: 273.4.bt
• Level: $273$
• Weight: $4$
• Character orbit: 273.bt
• Rep. character: $\chi_{273}(136,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $224$
• Sturm bound: $149$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.bt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(149\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(273, [\chi])\).

	Total	New	Old
Modular forms	464	224	240
Cusp forms	432	224	208
Eisenstein series	32	0	32

Trace form

224 * q + 40 * q^7 + 1008 * q^9 + 112 * q^11 + 192 * q^12 - 336 * q^14 - 3584 * q^16 - 768 * q^19 - 84 * q^21 + 112 * q^22 - 540 * q^24 + 1500 * q^26 - 820 * q^28 + 248 * q^29 - 180 * q^31 + 280 * q^32 - 520 * q^35 + 1120 * q^37 + 84 * q^39 + 2340 * q^40 - 2088 * q^41 - 468 * q^42 + 336 * q^43 + 1792 * q^44 + 2928 * q^46 - 1980 * q^49 + 2056 * q^50 + 360 * q^51 - 1584 * q^52 + 1720 * q^53 + 1656 * q^55 - 576 * q^56 + 504 * q^57 - 1984 * q^58 + 4128 * q^59 - 2868 * q^60 + 1800 * q^61 + 4176 * q^62 + 396 * q^63 + 2536 * q^65 - 240 * q^67 + 5024 * q^70 - 120 * q^71 + 3168 * q^73 + 4576 * q^74 + 4200 * q^75 - 432 * q^76 + 984 * q^78 - 832 * q^79 + 6348 * q^80 - 9072 * q^81 - 864 * q^82 + 3792 * q^83 - 3312 * q^84 - 1616 * q^85 - 4032 * q^86 - 8424 * q^88 - 4224 * q^89 + 1736 * q^91 - 12184 * q^92 + 3276 * q^93 - 14412 * q^94 - 4320 * q^96 + 1512 * q^97 - 5916 * q^98 + 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(273, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)