Space of modular forms of level 1400, weight 2, and Character 1400.ct

• Label: 1400.2.ct
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.ct
• Rep. character: $\chi_{1400}(13,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1888$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.ct (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1400 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

	Total	New	Old
Modular forms	1952	1952	0
Cusp forms	1888	1888	0
Eisenstein series	64	64	0

Trace form

1888 * q - 16 * q^2 - 20 * q^4 - 16 * q^7 - 4 * q^8 - 40 * q^9 - 10 * q^14 - 32 * q^15 - 12 * q^16 - 12 * q^18 - 24 * q^22 - 32 * q^23 - 32 * q^25 - 6 * q^28 + 24 * q^30 + 4 * q^32 - 44 * q^36 - 40 * q^39 - 50 * q^42 - 20 * q^44 - 12 * q^46 - 140 * q^50 - 6 * q^56 - 56 * q^57 + 48 * q^58 - 152 * q^60 - 32 * q^63 + 40 * q^64 - 32 * q^65 - 26 * q^70 - 24 * q^71 - 40 * q^72 + 52 * q^78 - 40 * q^79 + 384 * q^81 - 90 * q^84 - 12 * q^86 - 188 * q^88 + 4 * q^92 - 120 * q^95 - 170 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

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