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

• Label: 1936.2.bk
• Level: $1936$
• Weight: $2$
• Character orbit: 1936.bk
• Rep. character: $\chi_{1936}(49,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $2600$
• Sturm bound: $528$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1936.bk (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{55})\)
Sturm bound:			\(528\)

Dimensions

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

	Total	New	Old
Modular forms	10800	2680	8120
Cusp forms	10320	2600	7720
Eisenstein series	480	80	400

Trace form

2600 * q + 30 * q^3 - 41 * q^5 + 43 * q^7 - 656 * q^9 + 42 * q^11 - 41 * q^13 + 14 * q^15 - 37 * q^17 + 35 * q^19 - 9 * q^21 + 6 * q^23 + 28 * q^25 - 30 * q^27 - 49 * q^29 + 41 * q^31 - 16 * q^33 + 57 * q^35 - 29 * q^37 + 58 * q^39 - 57 * q^41 + 80 * q^43 + 36 * q^45 + 59 * q^47 + 14 * q^49 + 170 * q^51 - 65 * q^53 + 197 * q^55 - 2 * q^57 + 29 * q^59 - 33 * q^61 - 54 * q^63 - 38 * q^65 + 32 * q^67 + 17 * q^69 + 11 * q^71 - 41 * q^73 - 147 * q^77 + 75 * q^79 - 562 * q^81 - 19 * q^83 - 75 * q^85 - 99 * q^87 - 24 * q^89 + 19 * q^91 - 22 * q^93 + 37 * q^95 - 67 * q^97 - 134 * q^99

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

\( S_{2}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(968, [\chi])\)\(^{\oplus 2}\)