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

• Label: 272.4.v
• Level: $272$
• Weight: $4$
• Character orbit: 272.v
• Rep. character: $\chi_{272}(49,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $104$
• Sturm bound: $144$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	272.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
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	456	112	344
Cusp forms	408	104	304
Eisenstein series	48	8	40

Trace form

104 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 + 36 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 + 52 * q^19 + 4 * q^23 + 40 * q^25 + 4 * q^27 - 288 * q^29 + 4 * q^31 - 8 * q^33 - 1672 * q^35 - 4 * q^37 - 104 * q^39 + 232 * q^41 + 4 * q^43 + 176 * q^45 - 4 * q^49 + 1404 * q^51 + 568 * q^53 - 1460 * q^57 - 116 * q^59 - 2228 * q^61 + 3280 * q^63 + 1716 * q^65 + 1472 * q^67 - 2088 * q^69 + 1548 * q^71 + 736 * q^73 + 796 * q^75 + 364 * q^77 - 1556 * q^79 - 6588 * q^83 + 952 * q^85 - 5108 * q^87 - 1368 * q^91 + 1820 * q^93 + 4 * q^95 - 76 * q^97 + 7648 * 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.

Decomposition of \(S_{4}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)