Space of modular forms of level 3724, weight 2, and Character 3724.cz

• Label: 3724.2.cz
• Level: $3724$
• Weight: $2$
• Character orbit: 3724.cz
• Rep. character: $\chi_{3724}(297,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $1128$
• Sturm bound: $1120$

Defining parameters

Level:	\( N \)	\(=\)	\( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3724.cz (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 931 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3724, [\chi])\).

	Total	New	Old
Modular forms	6792	1128	5664
Cusp forms	6648	1128	5520
Eisenstein series	144	0	144

Trace form

1128 * q - 3 * q^5 - 2 * q^7 - 192 * q^9 - 10 * q^11 + 6 * q^13 + 9 * q^15 - 14 * q^17 - 3 * q^19 + 9 * q^21 + 4 * q^23 - 97 * q^25 + 6 * q^29 - 9 * q^31 + q^35 - 51 * q^37 - 18 * q^39 + 6 * q^41 + 2 * q^43 + 5 * q^45 - 42 * q^47 - 22 * q^49 + 6 * q^53 - 41 * q^55 - 3 * q^57 - 6 * q^59 - 56 * q^61 + 55 * q^63 - 3 * q^67 + 24 * q^69 + 9 * q^71 - 132 * q^75 - 22 * q^77 + 24 * q^79 - 188 * q^81 + 77 * q^83 + 71 * q^85 - 24 * q^87 - 159 * q^91 - 97 * q^93 - 38 * q^95 - 3 * q^97 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3724, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3724, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1862, [\chi])\)\(^{\oplus 2}\)