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

• Label: 1400.2.cx
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.cx
• Rep. character: $\chi_{1400}(221,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $1888$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.cx (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1400 \)
Character field:			\(\Q(\zeta_{30})\)
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 - 3 * q^2 - 3 * q^4 - 4 * q^6 - 32 * q^7 + 6 * q^8 - 234 * q^9 + 3 * q^10 + 9 * q^12 + 6 * q^14 - 20 * q^15 - 3 * q^16 - 6 * q^17 - 22 * q^18 - 20 * q^20 - 4 * q^22 - 6 * q^23 - 14 * q^24 - 8 * q^25 - 12 * q^26 - 20 * q^28 + 21 * q^30 - 30 * q^31 + 12 * q^32 + 18 * q^33 - 52 * q^34 - 76 * q^36 + 14 * q^38 - 18 * q^39 - 15 * q^40 - 24 * q^41 - 52 * q^42 + 13 * q^44 - 31 * q^46 - 30 * q^47 - 32 * q^48 - 32 * q^49 - 118 * q^50 - 98 * q^52 - 13 * q^54 - 12 * q^55 - 30 * q^56 - 40 * q^57 - 27 * q^58 + 25 * q^60 + 52 * q^62 + 42 * q^63 - 42 * q^64 - 18 * q^65 - 29 * q^66 - 46 * q^68 + 53 * q^70 - 24 * q^71 + 60 * q^72 - 6 * q^73 + 22 * q^74 - 76 * q^76 - 114 * q^78 - 6 * q^79 + 54 * q^80 + 186 * q^81 + 76 * q^82 + 39 * q^84 - 17 * q^86 - 18 * q^87 - 88 * q^88 - 6 * q^89 - 236 * q^90 + 26 * q^92 - 11 * q^94 + 24 * q^95 - 51 * q^96 + 24 * q^97 + 94 * 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.