Space of modular forms of level 1421, weight 2, and Character 1421.l

• Label: 1421.2.l
• Level: $1421$
• Weight: $2$
• Character orbit: 1421.l
• Rep. character: $\chi_{1421}(36,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $828$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1421.l (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1421 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1421, [\chi])\).

	Total	New	Old
Modular forms	852	852	0
Cusp forms	828	828	0
Eisenstein series	24	24	0

Trace form

828 * q - 3 * q^2 - 3 * q^3 - 139 * q^4 + q^5 + 3 * q^6 - q^7 + 5 * q^8 - 129 * q^9 + 13 * q^10 - 3 * q^11 - 25 * q^12 + q^13 - 7 * q^14 + 15 * q^15 - 127 * q^16 + 10 * q^17 - 4 * q^18 - 10 * q^19 + 33 * q^20 + 29 * q^21 + 26 * q^22 - 12 * q^23 - 10 * q^24 - 109 * q^25 + 18 * q^26 + 12 * q^27 - 117 * q^28 + q^29 - 84 * q^30 - 8 * q^31 + 41 * q^32 - 31 * q^33 + 10 * q^34 + 29 * q^35 - 113 * q^36 + 4 * q^37 + 12 * q^38 + 12 * q^39 + 41 * q^40 - 5 * q^41 - 50 * q^42 - 15 * q^43 + 51 * q^44 - 49 * q^46 + 6 * q^47 - 126 * q^48 - 3 * q^49 + 56 * q^50 + 21 * q^51 + 67 * q^52 + 29 * q^53 - 39 * q^54 - 36 * q^55 + 87 * q^56 - q^57 + 53 * q^58 + 24 * q^59 + 93 * q^60 - 123 * q^61 + 60 * q^62 + 78 * q^63 - 169 * q^64 - 27 * q^65 - 159 * q^66 - 16 * q^67 + 78 * q^68 - 7 * q^69 + 16 * q^70 - 44 * q^71 - 42 * q^72 - 9 * q^73 + 29 * q^74 + 67 * q^75 - q^76 + 38 * q^77 - 55 * q^78 - 90 * q^79 - 3 * q^80 - 120 * q^81 + 14 * q^82 + 44 * q^83 + 43 * q^84 + 7 * q^85 - 144 * q^86 + 59 * q^87 - 43 * q^88 - 126 * q^89 + 82 * q^90 + 12 * q^91 + 70 * q^92 + 21 * q^93 - 34 * q^94 + 61 * q^95 + 85 * q^96 - 40 * q^97 + 99 * q^98 + 92 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1421, [\chi])\) into newform subspaces

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