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

• Label: 1395.2.cf
• Level: $1395$
• Weight: $2$
• Character orbit: 1395.cf
• Rep. character: $\chi_{1395}(428,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $752$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1395.cf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1395 \)
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	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

752 * q - 12 * q^2 + 6 * q^3 - 6 * q^5 - 4 * q^6 + 2 * q^7 - 4 * q^10 + 12 * q^12 + 2 * q^13 + 344 * q^16 - 6 * q^18 - 4 * q^21 + 10 * q^22 - 12 * q^23 - 4 * q^25 + 12 * q^27 - 8 * q^28 + 30 * q^30 - 4 * q^31 - 120 * q^32 - 22 * q^33 - 36 * q^36 + 2 * q^37 + 78 * q^38 - 6 * q^40 + 12 * q^41 - 2 * q^42 + 2 * q^43 + 38 * q^45 - 56 * q^46 - 6 * q^47 + 78 * q^48 + 4 * q^51 - 28 * q^52 - 60 * q^53 + 22 * q^55 - 180 * q^56 + 26 * q^57 + 24 * q^58 + 12 * q^60 - 8 * q^61 + 54 * q^62 - 22 * q^63 - 6 * q^65 + 80 * q^66 - 4 * q^67 - 24 * q^70 + 60 * q^71 - 80 * q^72 - 4 * q^73 - 18 * q^75 + 48 * q^76 - 12 * q^77 - 68 * q^78 - 54 * q^80 - 108 * q^81 - 8 * q^82 - 4 * q^85 + 70 * q^87 - 12 * q^88 - 54 * q^90 - 32 * q^91 - 36 * q^92 - 96 * q^93 + 18 * q^95 + 172 * q^96 - 10 * q^97 - 168 * q^98

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

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