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

• Label: 1936.2.j
• Level: $1936$
• Weight: $2$
• Character orbit: 1936.j
• Rep. character: $\chi_{1936}(485,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $418$
• Sturm bound: $528$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1936.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(528\)

Dimensions

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

	Total	New	Old
Modular forms	552	454	98
Cusp forms	504	418	86
Eisenstein series	48	36	12

Trace form

418 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 8 * q^6 + 8 * q^8 + 4 * q^10 - 4 * q^12 + 2 * q^13 + 4 * q^14 + 12 * q^15 + 16 * q^16 + 4 * q^17 + 18 * q^18 + 10 * q^19 + 24 * q^20 - 4 * q^21 - 28 * q^24 - 4 * q^26 - 16 * q^27 - 28 * q^28 - 6 * q^29 - 8 * q^30 - 8 * q^31 + 12 * q^32 + 16 * q^34 - 20 * q^35 - 16 * q^36 - 6 * q^37 - 36 * q^38 + 16 * q^40 + 20 * q^42 - 10 * q^43 - 22 * q^45 + 40 * q^46 + 24 * q^47 - 28 * q^48 - 306 * q^49 - 58 * q^50 + 20 * q^51 + 40 * q^52 + 10 * q^53 - 32 * q^54 + 16 * q^56 - 28 * q^58 + 30 * q^59 - 68 * q^60 - 14 * q^61 - 16 * q^62 - 4 * q^63 + 24 * q^64 + 12 * q^65 + 14 * q^67 - 4 * q^68 - 20 * q^69 + 16 * q^70 + 16 * q^72 + 56 * q^74 + 110 * q^75 - 16 * q^76 - 104 * q^78 - 32 * q^79 - 20 * q^80 - 270 * q^81 - 4 * q^82 - 38 * q^83 - 68 * q^84 + 28 * q^85 + 8 * q^86 - 16 * q^90 - 4 * q^91 + 12 * q^92 + 32 * q^93 + 60 * q^95 - 20 * q^96 + 4 * q^97 - 66 * q^98

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

\( S_{2}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)