Space of modular forms of level 1596, weight 2, and Character 1596.de

• Label: 1596.2.de
• Level: $1596$
• Weight: $2$
• Character orbit: 1596.de
• Rep. character: $\chi_{1596}(25,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $162$
• Sturm bound: $640$

Defining parameters

Level:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1596.de (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{9})\)
Sturm bound:			\(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1596, [\chi])\).

	Total	New	Old
Modular forms	1992	162	1830
Cusp forms	1848	162	1686
Eisenstein series	144	0	144

Trace form

162 * q + 12 * q^7 - 12 * q^11 - 6 * q^13 + 24 * q^17 + 9 * q^19 - 3 * q^21 + 24 * q^23 + 36 * q^25 + 3 * q^27 + 12 * q^29 + 12 * q^37 - 12 * q^41 + 30 * q^43 + 6 * q^45 + 36 * q^49 - 12 * q^53 + 12 * q^57 + 48 * q^59 - 3 * q^61 + 12 * q^65 + 39 * q^67 + 48 * q^69 - 24 * q^71 + 3 * q^73 + 21 * q^75 - 30 * q^77 - 45 * q^79 - 12 * q^83 + 36 * q^85 + 96 * q^89 + 3 * q^91 - 42 * q^93 - 24 * q^95 + 42 * q^97 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1596, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1596, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)