Space of modular forms of level 1936, weight 2, and Character 1936.y

• Label: 1936.2.y
• Level: $1936$
• Weight: $2$
• Character orbit: 1936.y
• Rep. character: $\chi_{1936}(403,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1664$
• Sturm bound: $528$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1936.y (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 176 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1936, [\chi])\).

	Total	New	Old
Modular forms	2208	1792	416
Cusp forms	2016	1664	352
Eisenstein series	192	128	64

Trace form

1664 * q + 10 * q^2 + 6 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 + 20 * q^7 + 10 * q^8 - 48 * q^12 + 10 * q^13 + 4 * q^14 - 14 * q^16 + 20 * q^17 - 40 * q^18 + 10 * q^19 + 22 * q^20 - 144 * q^23 + 10 * q^24 - 56 * q^26 + 18 * q^27 + 10 * q^28 + 10 * q^29 + 50 * q^30 - 76 * q^34 + 10 * q^35 + 22 * q^36 + 30 * q^37 - 22 * q^38 + 20 * q^39 + 10 * q^40 - 10 * q^42 - 32 * q^45 + 30 * q^46 - 34 * q^48 + 332 * q^49 + 10 * q^50 + 10 * q^51 + 50 * q^52 - 18 * q^53 - 168 * q^56 - 14 * q^58 - 26 * q^59 - 22 * q^60 + 10 * q^61 + 10 * q^62 - 38 * q^64 - 24 * q^67 + 140 * q^68 + 24 * q^69 - 100 * q^70 - 52 * q^71 - 190 * q^72 - 40 * q^74 - 70 * q^75 - 172 * q^78 - 128 * q^80 + 300 * q^81 - 22 * q^82 + 110 * q^83 - 40 * q^84 + 10 * q^85 - 6 * q^86 - 60 * q^90 - 70 * q^91 - 90 * q^92 + 18 * q^93 - 180 * q^94 - 90 * q^96 + 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1936, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1936, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)