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

• Label: 350.4.m
• Level: $350$
• Weight: $4$
• Character orbit: 350.m
• Rep. character: $\chi_{350}(29,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $176$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(240\)

Dimensions

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

	Total	New	Old
Modular forms	736	176	560
Cusp forms	704	176	528
Eisenstein series	32	0	32

Trace form

176 * q + 176 * q^4 + 76 * q^5 + 488 * q^9 + 56 * q^10 + 44 * q^11 - 160 * q^12 - 56 * q^14 - 260 * q^15 - 704 * q^16 - 144 * q^19 + 256 * q^20 + 84 * q^21 + 360 * q^22 + 440 * q^23 + 1764 * q^25 - 368 * q^26 + 1080 * q^27 - 28 * q^29 + 80 * q^30 + 144 * q^31 - 1920 * q^33 - 960 * q^34 - 56 * q^35 - 1952 * q^36 - 1360 * q^37 - 732 * q^39 - 224 * q^40 + 112 * q^41 - 176 * q^44 - 408 * q^45 + 1016 * q^46 - 2080 * q^47 - 640 * q^48 - 8624 * q^49 - 456 * q^50 - 592 * q^51 + 2260 * q^53 + 1104 * q^54 - 2896 * q^55 + 224 * q^56 - 2808 * q^59 - 2560 * q^60 - 1288 * q^61 - 2660 * q^63 + 2816 * q^64 - 3956 * q^65 + 7560 * q^67 - 1336 * q^69 + 504 * q^70 - 1048 * q^71 + 5760 * q^73 + 4752 * q^74 + 3360 * q^75 - 384 * q^76 - 1120 * q^77 + 13280 * q^78 + 3760 * q^79 - 64 * q^80 + 1864 * q^81 - 4920 * q^83 - 336 * q^84 - 4868 * q^85 + 1720 * q^86 - 18780 * q^87 + 1256 * q^89 - 3048 * q^90 + 364 * q^91 - 3600 * q^92 + 3200 * q^95 - 5280 * q^97 + 1544 * 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

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