Space of modular forms of level 508, weight 4, and Character 508.j

• Label: 508.4.j
• Level: $508$
• Weight: $4$
• Character orbit: 508.j
• Rep. character: $\chi_{508}(37,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $192$
• Sturm bound: $256$

Defining parameters

Level:	\( N \)	\(=\)	\( 508 = 2^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	508.j (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 127 \)
Character field:			\(\Q(\zeta_{9})\)
Sturm bound:			\(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(508, [\chi])\).

	Total	New	Old
Modular forms	1170	192	978
Cusp forms	1134	192	942
Eisenstein series	36	0	36

Trace form

192 * q + 30 * q^5 + 18 * q^7 - 30 * q^11 - 6 * q^13 + 126 * q^15 - 96 * q^17 - 300 * q^21 + 108 * q^23 - 2112 * q^25 + 132 * q^29 + 1164 * q^31 + 504 * q^33 - 450 * q^35 - 798 * q^37 - 684 * q^39 + 54 * q^41 + 504 * q^43 + 138 * q^45 - 738 * q^47 + 366 * q^49 + 612 * q^51 + 756 * q^53 + 1926 * q^55 - 324 * q^57 + 606 * q^59 - 540 * q^61 + 4392 * q^63 + 1236 * q^65 - 606 * q^67 + 126 * q^69 + 2154 * q^71 + 990 * q^75 + 1872 * q^77 - 2862 * q^79 - 108 * q^81 - 612 * q^83 - 588 * q^85 + 8484 * q^87 + 3954 * q^89 + 7146 * q^91 - 6486 * q^93 - 5268 * q^95 - 8820 * q^97 + 1440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(508, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(508, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(508, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(254, [\chi])\)\(^{\oplus 2}\)