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

• Label: 350.4.h
• Level: $350$
• Weight: $4$
• Character orbit: 350.h
• Rep. character: $\chi_{350}(71,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $184$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(240\)

Dimensions

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

	Total	New	Old
Modular forms	736	184	552
Cusp forms	704	184	520
Eisenstein series	32	0	32

Trace form

184 * q + 4 * q^2 - 16 * q^3 - 184 * q^4 - 54 * q^5 + 16 * q^8 - 322 * q^9 - 4 * q^10 - 44 * q^11 + 96 * q^12 - 116 * q^13 - 56 * q^14 + 268 * q^15 - 736 * q^16 + 68 * q^17 - 736 * q^18 - 144 * q^19 - 96 * q^20 - 84 * q^21 + 216 * q^22 + 832 * q^23 + 490 * q^25 - 72 * q^26 + 944 * q^27 - 288 * q^29 - 272 * q^30 - 144 * q^31 - 256 * q^32 - 856 * q^33 - 1020 * q^34 + 56 * q^35 - 1288 * q^36 + 678 * q^37 - 48 * q^38 - 732 * q^39 - 16 * q^40 + 348 * q^41 + 1552 * q^43 - 176 * q^44 - 578 * q^45 - 1016 * q^46 + 4088 * q^47 + 384 * q^48 + 9016 * q^49 + 204 * q^50 + 592 * q^51 - 464 * q^52 - 2518 * q^53 + 1104 * q^54 + 3344 * q^55 - 224 * q^56 - 1584 * q^57 + 1336 * q^58 - 2808 * q^59 - 2528 * q^60 + 2948 * q^61 + 32 * q^62 - 1596 * q^63 - 2944 * q^64 - 1126 * q^65 - 3784 * q^67 + 272 * q^68 + 6824 * q^69 + 504 * q^70 - 3912 * q^71 + 656 * q^72 + 5404 * q^73 + 7192 * q^74 + 120 * q^75 + 384 * q^76 + 672 * q^77 + 896 * q^78 + 3760 * q^79 + 416 * q^80 - 11714 * q^81 - 1176 * q^82 + 1984 * q^83 - 336 * q^84 - 5222 * q^85 - 1720 * q^86 - 1308 * q^87 - 576 * q^88 - 4394 * q^89 - 1748 * q^90 - 364 * q^91 - 4112 * q^92 - 5344 * q^93 - 3256 * q^95 + 9412 * q^97 + 196 * q^98 + 3304 * q^99

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

\( S_{4}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)