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

• Label: 1950.4.ci
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.ci
• Rep. character: $\chi_{1950}(697,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1680$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.ci (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(1680\)

Dimensions

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

	Total	New	Old
Modular forms	10144	1680	8464
Cusp forms	10016	1680	8336
Eisenstein series	128	0	128

Trace form

1680 * q + 1680 * q^4 + 20 * q^5 + 44 * q^13 - 48 * q^15 - 6720 * q^16 + 52 * q^17 + 288 * q^18 + 240 * q^19 + 320 * q^20 - 352 * q^23 + 412 * q^25 + 320 * q^29 + 1920 * q^33 - 720 * q^34 - 504 * q^37 - 2380 * q^41 - 1856 * q^43 + 216 * q^45 - 96 * q^47 + 82320 * q^49 + 1120 * q^50 - 176 * q^52 - 1980 * q^53 + 1872 * q^55 - 240 * q^58 + 192 * q^60 + 26880 * q^64 - 5868 * q^65 - 208 * q^68 + 1584 * q^70 + 288 * q^72 + 4560 * q^73 + 624 * q^77 + 672 * q^78 + 320 * q^80 + 34020 * q^81 + 312 * q^82 - 1824 * q^83 + 5576 * q^85 + 3744 * q^87 + 4900 * q^89 - 936 * q^90 + 7920 * q^91 + 1408 * q^92 + 6592 * q^95 - 13120 * 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

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