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

• Label: 1421.2.bw
• Level: $1421$
• Weight: $2$
• Character orbit: 1421.bw
• Rep. character: $\chi_{1421}(88,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $1560$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 1421 = 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1421.bw (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(280\)

Dimensions

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

	Total	New	Old
Modular forms	1704	1560	144
Cusp forms	1656	1560	96
Eisenstein series	48	0	48

Trace form

1560 * q + 2 * q^3 + 128 * q^4 - 2 * q^5 + 12 * q^8 + 128 * q^9 - 2 * q^10 - 20 * q^11 - 76 * q^12 + 16 * q^13 - 66 * q^14 + 116 * q^16 - 2 * q^17 - 18 * q^18 - 54 * q^19 - 48 * q^20 + 12 * q^22 - 8 * q^23 - 28 * q^24 + 124 * q^25 - 12 * q^26 + 8 * q^27 - 46 * q^28 - 12 * q^30 - 74 * q^31 - 106 * q^32 - 18 * q^33 - 64 * q^34 - 40 * q^35 - 200 * q^36 - 42 * q^37 - 26 * q^38 + 6 * q^39 - 20 * q^40 - 8 * q^41 - 56 * q^42 + 24 * q^43 + 84 * q^44 - 48 * q^45 - 24 * q^46 + 6 * q^47 + 56 * q^48 + 96 * q^49 + 44 * q^50 + 72 * q^51 + 126 * q^52 - 88 * q^53 - 38 * q^54 + 100 * q^55 + 24 * q^56 + 44 * q^57 - 36 * q^59 - 244 * q^60 - 16 * q^61 + 48 * q^62 - 132 * q^63 - 288 * q^64 - 38 * q^65 - 284 * q^66 - 30 * q^67 - 160 * q^68 - 108 * q^69 - 166 * q^70 - 80 * q^71 - 284 * q^72 - 16 * q^73 - 90 * q^74 - 44 * q^75 - 158 * q^76 - 38 * q^77 - 92 * q^78 - 26 * q^79 + 30 * q^80 + 226 * q^81 - 148 * q^82 - 44 * q^83 + 32 * q^84 - 20 * q^85 - 104 * q^86 + 12 * q^87 + 250 * q^88 + 42 * q^89 + 324 * q^90 - 202 * q^91 - 24 * q^92 + 170 * q^93 - 68 * q^94 - 14 * q^95 - 104 * q^96 - 72 * q^97 + 298 * q^98 - 132 * 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.

Decomposition of \(S_{2}^{\mathrm{old}}(1421, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1421, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)