Space of modular forms of level 350, weight 4, and Character 350.x

• Label: 350.4.x
• Level: $350$
• Weight: $4$
• Character orbit: 350.x
• Rep. character: $\chi_{350}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $960$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(350, [\chi])\).

	Total	New	Old
Modular forms	2944	960	1984
Cusp forms	2816	960	1856
Eisenstein series	128	0	128

Trace form

960 * q - 48 * q^5 + 4 * q^7 + 72 * q^10 + 504 * q^15 - 1920 * q^16 - 288 * q^17 - 16 * q^18 + 816 * q^22 - 628 * q^23 - 152 * q^25 + 128 * q^28 + 320 * q^29 + 360 * q^30 + 1956 * q^33 - 1088 * q^35 + 8640 * q^36 + 552 * q^37 + 528 * q^38 - 2440 * q^39 + 488 * q^42 - 2736 * q^43 + 2832 * q^45 - 1464 * q^47 - 448 * q^50 + 2384 * q^53 + 1344 * q^57 - 1024 * q^58 - 4920 * q^59 + 352 * q^60 + 1828 * q^63 + 468 * q^65 + 1936 * q^67 + 4608 * q^68 - 3528 * q^70 - 64 * q^72 + 5616 * q^73 + 30288 * q^75 - 3972 * q^77 + 4192 * q^78 - 768 * q^80 - 9720 * q^81 + 3456 * q^82 + 960 * q^84 + 776 * q^85 - 15732 * q^87 - 1248 * q^88 - 40800 * q^89 - 2016 * q^92 + 2136 * q^93 - 600 * q^95 + 400 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)