Space of modular forms of level 1395, weight 2, and Character 1395.ck

• Label: 1395.2.ck
• Level: $1395$
• Weight: $2$
• Character orbit: 1395.ck
• Rep. character: $\chi_{1395}(32,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $720$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1395.ck (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1395, [\chi])\).

	Total	New	Old
Modular forms	784	720	64
Cusp forms	752	720	32
Eisenstein series	32	0	32

Trace form

720 * q - 16 * q^6 - 24 * q^11 - 12 * q^15 + 360 * q^16 - 72 * q^18 + 8 * q^21 - 48 * q^23 + 12 * q^27 + 20 * q^33 + 48 * q^36 + 64 * q^42 + 44 * q^45 - 48 * q^46 + 24 * q^48 + 96 * q^50 - 104 * q^51 + 72 * q^56 + 8 * q^57 + 48 * q^60 - 24 * q^61 - 52 * q^63 - 144 * q^65 - 112 * q^66 - 144 * q^68 - 152 * q^72 - 144 * q^75 + 148 * q^78 + 48 * q^81 - 96 * q^82 - 48 * q^85 + 72 * q^86 - 20 * q^87 - 48 * q^88 + 120 * q^90 + 48 * q^91 + 84 * q^92 - 8 * q^96 - 48 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1395, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1395, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1395, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)