Space of modular forms of level 1296, weight 2, and Character 1296.bg

• Label: 1296.2.bg
• Level: $1296$
• Weight: $2$
• Character orbit: 1296.bg
• Rep. character: $\chi_{1296}(49,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $954$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1296.bg (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1296, [\chi])\).

	Total	New	Old
Modular forms	3996	990	3006
Cusp forms	3780	954	2826
Eisenstein series	216	36	180

Trace form

954 * q + 18 * q^3 - 18 * q^5 + 18 * q^7 - 18 * q^9 + 18 * q^11 - 18 * q^13 + 18 * q^15 - 18 * q^17 + 18 * q^19 - 18 * q^21 + 18 * q^23 - 18 * q^25 + 18 * q^27 - 18 * q^29 + 18 * q^31 - 18 * q^33 + 18 * q^35 - 18 * q^37 + 18 * q^39 - 18 * q^41 + 18 * q^43 - 18 * q^45 + 18 * q^47 - 18 * q^49 + 18 * q^51 - 9 * q^53 + 9 * q^55 - 18 * q^57 + 18 * q^59 - 18 * q^61 + 18 * q^63 - 18 * q^65 + 18 * q^67 - 18 * q^69 + 18 * q^71 - 18 * q^73 + 18 * q^75 - 18 * q^77 + 18 * q^79 - 18 * q^81 + 18 * q^83 - 18 * q^85 + 18 * q^87 - 36 * q^89 + 18 * q^91 - 18 * q^93 + 180 * q^95 - 18 * q^97 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1296, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)