Space of modular forms of level 272, weight 4, and Character 272.w

• Label: 272.4.w
• Level: $272$
• Weight: $4$
• Character orbit: 272.w
• Rep. character: $\chi_{272}(189,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $424$
• Sturm bound: $144$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	272.w (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 272 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(272, [\chi])\).

	Total	New	Old
Modular forms	440	440	0
Cusp forms	424	424	0
Eisenstein series	16	16	0

Trace form

424 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 28 * q^6 - 4 * q^8 - 36 * q^10 - 4 * q^11 - 224 * q^12 - 112 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 468 * q^22 + 292 * q^24 + 396 * q^26 - 112 * q^27 + 532 * q^28 - 4 * q^29 - 8 * q^31 + 476 * q^32 - 16 * q^33 - 756 * q^34 - 8 * q^35 - 1124 * q^36 - 4 * q^37 + 64 * q^38 - 272 * q^40 + 2480 * q^42 + 1328 * q^44 + 604 * q^45 - 100 * q^46 - 1200 * q^48 - 8 * q^49 - 8 * q^50 + 1396 * q^51 - 8 * q^52 - 8 * q^53 - 680 * q^54 + 3520 * q^55 - 272 * q^56 + 216 * q^57 + 28 * q^58 - 496 * q^60 - 1828 * q^61 + 3176 * q^62 - 8 * q^63 - 984 * q^65 + 5804 * q^66 - 8 * q^67 + 2048 * q^68 - 8 * q^69 + 5880 * q^70 - 3880 * q^72 + 3604 * q^74 - 612 * q^75 - 1328 * q^76 - 8 * q^77 + 448 * q^78 - 8 * q^79 + 1360 * q^80 - 28 * q^82 - 8 * q^84 - 4 * q^85 - 944 * q^86 - 1288 * q^88 - 6152 * q^90 - 3280 * q^91 - 260 * q^92 - 8 * q^93 + 3672 * q^94 - 8 * q^95 + 4280 * q^96 - 8 * q^97 - 13072 * q^98 + 2804 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(272, [\chi])\) into newform subspaces

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