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

• Label: 1950.4.da
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.da
• Rep. character: $\chi_{1950}(67,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $3360$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.da (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(1680\)

Dimensions

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

	Total	New	Old
Modular forms	20288	3360	16928
Cusp forms	20032	3360	16672
Eisenstein series	256	0	256

Trace form

3360 * q + 8 * q^2 + 1680 * q^4 - 24 * q^5 - 64 * q^8 + 152 * q^13 - 48 * q^15 + 6720 * q^16 - 308 * q^17 - 240 * q^19 + 384 * q^20 - 352 * q^23 - 356 * q^25 - 320 * q^29 - 512 * q^32 - 2304 * q^33 + 600 * q^34 + 1036 * q^37 + 4300 * q^41 + 16 * q^43 - 360 * q^45 + 82320 * q^49 - 1072 * q^50 - 64 * q^52 + 5244 * q^53 - 12312 * q^55 - 2016 * q^58 - 192 * q^60 - 4176 * q^62 - 53760 * q^64 - 2824 * q^65 - 3896 * q^67 + 1024 * q^68 - 6144 * q^70 - 5288 * q^73 - 7320 * q^74 + 624 * q^77 + 672 * q^78 + 768 * q^80 - 34020 * q^81 - 2160 * q^82 + 2916 * q^85 + 504 * q^87 + 5120 * q^89 - 936 * q^90 - 15840 * q^91 + 2816 * q^92 + 15328 * q^95 + 1240 * q^97 + 20088 * q^98

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

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