Space of modular forms of level 1352, weight 2, and Character 1352.bi

• Label: 1352.2.bi
• Level: $1352$
• Weight: $2$
• Character orbit: 1352.bi
• Rep. character: $\chi_{1352}(83,\cdot)$
• Character field: $\Q(\zeta_{52})$
• Dimension: $4320$
• Sturm bound: $364$

Defining parameters

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.bi (of order \(52\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1352 \)
Character field:			\(\Q(\zeta_{52})\)
Sturm bound:			\(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1352, [\chi])\).

	Total	New	Old
Modular forms	4416	4416	0
Cusp forms	4320	4320	0
Eisenstein series	96	96	0

Trace form

4320 * q - 24 * q^2 - 44 * q^3 - 26 * q^4 - 26 * q^6 - 30 * q^8 - 396 * q^9 - 26 * q^10 - 48 * q^11 - 26 * q^12 - 6 * q^14 - 22 * q^16 - 52 * q^17 - 8 * q^18 - 48 * q^19 - 34 * q^20 - 28 * q^22 - 22 * q^24 - 52 * q^25 + 8 * q^26 - 20 * q^27 - 38 * q^28 - 26 * q^30 + 96 * q^32 - 36 * q^33 - 42 * q^34 - 44 * q^35 - 26 * q^36 + 104 * q^38 - 62 * q^40 - 52 * q^41 - 34 * q^42 - 52 * q^43 - 66 * q^44 - 98 * q^46 - 42 * q^48 - 52 * q^49 - 52 * q^51 + 68 * q^52 - 30 * q^54 - 26 * q^56 - 52 * q^57 - 38 * q^58 - 104 * q^59 + 30 * q^60 - 156 * q^62 - 26 * q^64 - 44 * q^65 - 140 * q^66 - 48 * q^67 + 14 * q^68 - 86 * q^70 + 34 * q^72 - 52 * q^73 - 78 * q^74 - 52 * q^75 - 54 * q^76 + 166 * q^78 - 14 * q^80 - 348 * q^81 - 286 * q^82 - 88 * q^83 + 34 * q^84 + 6 * q^86 - 26 * q^88 - 28 * q^89 - 26 * q^90 - 32 * q^91 - 74 * q^92 + 142 * q^94 - 264 * q^96 - 36 * q^97 - 24 * q^98 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1352, [\chi])\) into newform subspaces

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