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

• Label: 272.4.s
• Level: $272$
• Weight: $4$
• Character orbit: 272.s
• Rep. character: $\chi_{272}(149,\cdot)$
• 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.s (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^3 - 4 * q^4 - 30 * q^6 + 1836 * q^9 + 74 * q^10 - 4 * q^11 + 54 * q^12 - 4 * q^13 + 36 * q^14 - 268 * q^16 - 4 * q^17 - 36 * q^18 + 166 * q^20 - 4 * q^21 - 270 * q^22 - 714 * q^24 - 4900 * q^25 - 500 * q^26 - 112 * q^27 - 532 * q^28 - 4 * q^29 - 552 * q^30 - 4 * q^31 - 460 * q^32 - 8 * q^33 + 194 * q^34 - 4 * q^35 - 108 * q^36 - 4 * q^38 - 108 * q^39 + 778 * q^40 + 32 * q^42 + 702 * q^44 - 1532 * q^46 + 1872 * q^47 + 14 * q^48 - 36 * q^50 - 1500 * q^51 + 1652 * q^52 - 540 * q^54 - 3012 * q^56 - 108 * q^57 + 1498 * q^58 + 1376 * q^59 + 3932 * q^60 + 800 * q^62 - 1376 * q^63 - 1516 * q^64 - 492 * q^65 - 1452 * q^66 - 4 * q^67 + 1146 * q^68 - 1060 * q^69 - 580 * q^70 - 2052 * q^72 - 296 * q^73 - 3534 * q^74 + 388 * q^75 + 2352 * q^76 - 1372 * q^77 - 3252 * q^78 + 2828 * q^79 - 3290 * q^80 + 14572 * q^81 - 2004 * q^82 - 4 * q^84 + 488 * q^85 + 6024 * q^86 - 4392 * q^87 - 2458 * q^88 + 1742 * q^90 - 3928 * q^91 - 4544 * q^92 - 108 * q^93 + 648 * q^94 - 4 * q^95 + 850 * q^96 - 4 * q^97 + 6080 * q^98 - 3028 * 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.