Space of modular forms of level 2100, weight 2, and Character 2100.z

• Label: 2100.2.z
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.z
• Rep. character: $\chi_{2100}(421,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $128$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.z (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

	Total	New	Old
Modular forms	1968	128	1840
Cusp forms	1872	128	1744
Eisenstein series	96	0	96

Trace form

128 * q - 4 * q^5 - 32 * q^9 + 4 * q^15 - 8 * q^17 - 12 * q^19 - 4 * q^21 - 12 * q^23 - 20 * q^25 - 36 * q^29 - 12 * q^33 + 4 * q^35 + 4 * q^37 - 24 * q^41 + 16 * q^43 - 4 * q^45 + 48 * q^47 + 128 * q^49 + 32 * q^51 + 24 * q^53 + 20 * q^55 + 8 * q^57 + 24 * q^59 - 48 * q^61 + 36 * q^65 - 24 * q^67 + 8 * q^69 + 64 * q^71 - 8 * q^73 + 16 * q^75 - 24 * q^77 - 16 * q^79 - 32 * q^81 - 12 * q^83 + 4 * q^85 + 24 * q^87 + 60 * q^89 - 8 * q^91 + 48 * q^93 + 44 * q^95 - 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

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