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

• Label: 1950.4.bg
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.bg
• Rep. character: $\chi_{1950}(181,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $832$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bg (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1680\)

Dimensions

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

	Total	New	Old
Modular forms	5072	832	4240
Cusp forms	5008	832	4176
Eisenstein series	64	0	64

Trace form

832 * q + 832 * q^4 - 1872 * q^9 - 64 * q^10 - 136 * q^13 - 3328 * q^16 + 240 * q^17 - 528 * q^23 - 696 * q^25 + 368 * q^26 - 448 * q^29 + 928 * q^35 + 7488 * q^36 + 256 * q^40 - 1856 * q^43 - 37632 * q^49 + 1632 * q^51 + 544 * q^52 - 6984 * q^53 - 5016 * q^55 - 40 * q^61 + 4176 * q^62 + 13312 * q^64 - 2960 * q^65 + 1056 * q^66 - 960 * q^68 - 3600 * q^69 - 1504 * q^74 + 624 * q^75 + 7728 * q^77 + 672 * q^78 + 2336 * q^79 - 16848 * q^81 + 3584 * q^82 - 2376 * q^87 - 576 * q^90 - 5448 * q^91 - 1408 * q^92 + 2816 * q^94 + 7536 * q^95

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

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