Space of modular forms of level 1950, weight 4, and Character 1950.v

• Label: 1950.4.v
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.v
• Rep. character: $\chi_{1950}(391,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $720$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.v (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1950, [\chi])\).

	Total	New	Old
Modular forms	5072	720	4352
Cusp forms	5008	720	4288
Eisenstein series	64	0	64

Trace form

720 * q - 720 * q^4 + 32 * q^5 + 24 * q^6 - 8 * q^7 - 1620 * q^9 - 24 * q^10 + 336 * q^11 - 84 * q^15 - 2880 * q^16 + 768 * q^17 + 152 * q^19 + 128 * q^20 + 168 * q^21 - 768 * q^22 - 696 * q^23 - 384 * q^24 - 164 * q^25 - 272 * q^28 - 96 * q^29 + 192 * q^30 + 828 * q^31 - 24 * q^33 + 544 * q^34 + 2904 * q^35 - 6480 * q^36 - 432 * q^37 + 704 * q^38 - 96 * q^40 + 1224 * q^42 - 832 * q^43 - 896 * q^44 + 288 * q^45 + 2032 * q^46 - 4016 * q^47 + 35256 * q^49 + 320 * q^50 + 1632 * q^53 + 216 * q^54 - 1376 * q^55 + 144 * q^57 + 336 * q^58 + 1968 * q^59 + 1344 * q^60 - 4352 * q^61 - 64 * q^62 + 648 * q^63 - 11520 * q^64 - 832 * q^65 - 864 * q^67 - 2048 * q^68 - 3032 * q^70 + 1392 * q^71 - 5208 * q^73 + 960 * q^75 - 2432 * q^76 - 2224 * q^77 - 5096 * q^79 + 512 * q^80 - 14580 * q^81 - 1984 * q^82 - 5368 * q^83 + 672 * q^84 + 7064 * q^85 - 1896 * q^87 + 3168 * q^88 + 3072 * q^89 - 216 * q^90 + 728 * q^91 + 1856 * q^92 - 3264 * q^93 + 3296 * q^95 + 384 * q^96 - 9756 * q^97 - 5056 * q^98 - 2016 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)