Space of modular forms of level 435, weight 4, and Character 435.s

• Label: 435.4.s
• Level: $435$
• Weight: $4$
• Character orbit: 435.s
• Rep. character: $\chi_{435}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $180$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(435, [\chi])\).

	Total	New	Old
Modular forms	368	180	188
Cusp forms	352	180	172
Eisenstein series	16	0	16

Trace form

180 * q + 8 * q^2 + 720 * q^4 + 96 * q^8 - 1620 * q^9 + 88 * q^10 - 180 * q^13 + 108 * q^15 + 2880 * q^16 + 552 * q^17 - 72 * q^18 - 308 * q^25 + 440 * q^26 + 392 * q^31 + 896 * q^32 + 72 * q^33 - 288 * q^34 - 992 * q^35 - 6480 * q^36 - 704 * q^38 - 24 * q^39 + 44 * q^40 + 396 * q^41 + 816 * q^42 + 2064 * q^44 - 1920 * q^46 - 1424 * q^50 - 1040 * q^52 + 1332 * q^53 - 432 * q^55 - 336 * q^56 - 768 * q^57 + 1228 * q^58 + 2616 * q^60 - 1660 * q^61 + 936 * q^62 + 14544 * q^64 + 2108 * q^65 + 1992 * q^66 + 96 * q^67 + 2408 * q^68 + 1148 * q^70 - 864 * q^72 + 3288 * q^73 - 576 * q^75 + 2792 * q^76 + 2208 * q^77 - 144 * q^78 + 936 * q^79 - 4984 * q^80 + 14580 * q^81 - 3232 * q^82 + 3616 * q^83 + 72 * q^84 + 1200 * q^85 - 972 * q^87 + 1584 * q^88 + 1932 * q^89 - 792 * q^90 - 1720 * q^92 + 6992 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(435, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)