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

• Label: 1950.4.bc
• Level: $1950$
• Weight: $4$
• Character orbit: 1950.bc
• Rep. character: $\chi_{1950}(751,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $268$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1680\)

Dimensions

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

	Total	New	Old
Modular forms	2568	268	2300
Cusp forms	2472	268	2204
Eisenstein series	96	0	96

Trace form

268 * q + 6 * q^3 + 536 * q^4 - 18 * q^7 - 1206 * q^9 + 204 * q^11 + 48 * q^12 - 94 * q^13 + 96 * q^14 - 2144 * q^16 + 32 * q^17 - 324 * q^19 + 144 * q^22 + 4 * q^23 - 88 * q^26 - 108 * q^27 - 72 * q^28 + 296 * q^29 - 576 * q^33 + 4824 * q^36 + 1092 * q^37 + 288 * q^38 + 72 * q^39 + 1788 * q^41 + 168 * q^42 - 98 * q^43 - 144 * q^46 + 96 * q^48 + 5812 * q^49 + 144 * q^51 - 152 * q^52 + 3632 * q^53 + 192 * q^56 + 24 * q^58 - 1284 * q^59 - 1690 * q^61 - 1232 * q^62 + 162 * q^63 - 17152 * q^64 + 432 * q^66 - 3606 * q^67 - 128 * q^68 + 24 * q^69 - 1548 * q^71 + 2792 * q^74 - 1296 * q^76 + 7864 * q^77 - 864 * q^78 + 5716 * q^79 - 10854 * q^81 - 216 * q^82 + 1368 * q^84 - 1368 * q^87 - 576 * q^88 - 4728 * q^89 + 4418 * q^91 + 32 * q^92 + 2646 * q^93 - 1712 * q^94 - 4170 * q^97 + 4752 * 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

\( S_{4}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)