Space of modular forms of level 2100, weight 4, and Character 2100.z

• Label: 2100.4.z
• Level: $2100$
• Weight: $4$
• Character orbit: 2100.z
• Rep. character: $\chi_{2100}(421,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $352$
• Sturm bound: $1920$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2100.z (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2100, [\chi])\).

	Total	New	Old
Modular forms	5808	352	5456
Cusp forms	5712	352	5360
Eisenstein series	96	0	96

Trace form

352 * q - 20 * q^5 - 792 * q^9 - 200 * q^13 - 24 * q^15 - 136 * q^17 - 72 * q^19 + 84 * q^21 + 264 * q^23 - 512 * q^25 + 24 * q^29 - 576 * q^33 + 56 * q^35 + 228 * q^37 - 696 * q^41 + 928 * q^43 - 180 * q^45 - 2064 * q^47 + 17248 * q^49 - 1632 * q^51 - 1428 * q^53 + 1328 * q^55 - 1464 * q^57 - 816 * q^59 - 952 * q^61 + 492 * q^65 - 448 * q^67 + 1248 * q^69 + 656 * q^71 + 1336 * q^73 - 480 * q^75 + 672 * q^77 + 2464 * q^79 - 7128 * q^81 + 3864 * q^83 - 908 * q^85 + 1368 * q^87 + 3540 * q^89 + 728 * q^91 - 2016 * q^93 - 7832 * q^95 + 3544 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)