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

• Label: 272.4.j
• Level: $272$
• Weight: $4$
• Character orbit: 272.j
• Rep. character: $\chi_{272}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $212$
• Sturm bound: $144$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	220	220	0
Cusp forms	212	212	0
Eisenstein series	8	8	0

Trace form

212 * q - 4 * q^4 - 4 * q^5 + 26 * q^6 - 1836 * q^9 + 42 * q^10 - 58 * q^12 - 4 * q^13 + 136 * q^14 - 268 * q^16 - 4 * q^17 - 36 * q^18 - 90 * q^20 - 4 * q^21 - 238 * q^22 - 246 * q^24 + 4900 * q^25 + 500 * q^26 + 332 * q^28 - 552 * q^30 - 4 * q^31 + 460 * q^32 - 8 * q^33 - 166 * q^34 - 4 * q^35 + 108 * q^36 - 4 * q^37 - 4 * q^38 + 108 * q^39 - 1070 * q^40 - 32 * q^42 + 1058 * q^44 - 396 * q^45 - 548 * q^46 + 1872 * q^47 + 1370 * q^48 - 36 * q^50 + 96 * q^51 + 1652 * q^52 - 1192 * q^54 + 96 * q^56 + 108 * q^57 + 1886 * q^58 - 1376 * q^59 - 3932 * q^60 + 1820 * q^61 - 2236 * q^62 - 1376 * q^63 - 1516 * q^64 - 492 * q^65 + 1452 * q^66 - 4 * q^67 + 614 * q^68 - 1060 * q^69 + 580 * q^70 - 2052 * q^72 + 296 * q^73 - 4166 * q^74 - 2352 * q^76 + 1372 * q^77 + 1196 * q^78 + 2828 * q^79 - 1298 * q^80 + 14572 * q^81 - 952 * q^82 - 4 * q^84 - 492 * q^85 + 6024 * q^86 + 4392 * q^87 + 22 * q^88 - 9766 * q^90 - 2208 * q^92 + 108 * q^93 - 648 * q^94 - 4 * q^95 - 7314 * q^96 - 4 * q^97 + 6080 * q^98

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

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