Space of modular forms of level 950, weight 4, and Character 950.h

• Label: 950.4.h
• Level: $950$
• Weight: $4$
• Character orbit: 950.h
• Rep. character: $\chi_{950}(191,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $544$
• Sturm bound: $600$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(950, [\chi])\).

	Total	New	Old
Modular forms	1816	544	1272
Cusp forms	1784	544	1240
Eisenstein series	32	0	32

Trace form

544 * q + 4 * q^2 - 16 * q^3 - 544 * q^4 - 62 * q^5 - 24 * q^6 - 16 * q^7 + 16 * q^8 - 1132 * q^9 + 20 * q^10 - 128 * q^11 + 96 * q^12 + 76 * q^13 + 224 * q^15 - 2176 * q^16 - 124 * q^17 - 720 * q^18 - 38 * q^19 - 128 * q^20 + 336 * q^22 + 506 * q^23 + 384 * q^24 + 1386 * q^25 + 1176 * q^26 + 392 * q^27 + 176 * q^28 + 12 * q^29 - 168 * q^30 - 972 * q^31 - 256 * q^32 + 2648 * q^33 - 1020 * q^34 - 1546 * q^35 - 4528 * q^36 - 210 * q^37 - 560 * q^39 + 80 * q^40 + 924 * q^41 - 696 * q^42 - 840 * q^43 + 48 * q^44 + 934 * q^45 + 1312 * q^47 + 384 * q^48 + 28152 * q^49 - 268 * q^50 + 1176 * q^51 + 304 * q^52 + 1554 * q^53 - 864 * q^54 + 970 * q^55 - 360 * q^58 - 1992 * q^59 - 3504 * q^60 + 1144 * q^61 - 864 * q^62 - 8356 * q^63 - 8704 * q^64 - 1882 * q^65 - 1056 * q^66 - 5688 * q^67 + 784 * q^68 + 8024 * q^69 + 4176 * q^70 - 2480 * q^71 + 720 * q^72 + 7156 * q^73 + 7608 * q^74 + 4724 * q^75 + 608 * q^76 + 2452 * q^77 + 3720 * q^78 + 3264 * q^79 + 288 * q^80 - 18776 * q^81 + 136 * q^82 - 2750 * q^83 - 11328 * q^85 + 336 * q^86 - 1848 * q^87 - 2016 * q^88 - 11018 * q^89 - 7372 * q^90 + 8256 * q^91 - 2896 * q^92 - 6568 * q^93 + 532 * q^95 - 384 * q^96 + 3880 * q^97 + 1764 * q^98 + 8192 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(950, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)