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

• Label: 1395.2.j
• Level: $1395$
• Weight: $2$
• Character orbit: 1395.j
• Rep. character: $\chi_{1395}(211,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $256$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1395.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 279 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	392	256	136
Cusp forms	376	256	120
Eisenstein series	16	0	16

Trace form

256 * q - 128 * q^4 + 6 * q^6 + 2 * q^7 + 12 * q^8 - 12 * q^12 - 4 * q^13 - 128 * q^16 - 16 * q^17 - 10 * q^18 - 4 * q^19 + 14 * q^21 - 30 * q^23 + 12 * q^24 - 128 * q^25 - 32 * q^26 + 18 * q^27 + 8 * q^28 - 8 * q^31 - 12 * q^32 - 4 * q^33 - 12 * q^34 + 6 * q^36 - 4 * q^37 + 8 * q^39 - 12 * q^40 + 16 * q^41 - 60 * q^42 + 8 * q^43 + 44 * q^44 - 4 * q^45 - 12 * q^46 + 76 * q^48 - 126 * q^49 + 16 * q^51 + 68 * q^52 - 16 * q^53 - 96 * q^54 + 28 * q^56 + 20 * q^57 - 18 * q^58 - 32 * q^59 + 14 * q^60 + 14 * q^61 - 44 * q^62 - 20 * q^63 + 316 * q^64 - 16 * q^65 + 22 * q^66 + 14 * q^67 + 148 * q^68 + 64 * q^69 + 32 * q^71 + 42 * q^72 + 14 * q^73 + 20 * q^74 + 20 * q^76 + 28 * q^77 - 136 * q^78 + 2 * q^79 + 44 * q^81 + 36 * q^82 + 112 * q^83 + 54 * q^84 + 240 * q^86 - 58 * q^87 - 16 * q^89 + 8 * q^90 - 44 * q^91 - 72 * q^92 + 36 * q^94 + 4 * q^95 - 28 * q^96 + 2 * q^97 + 42 * q^98 - 60 * q^99

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

\( S_{2}^{\mathrm{old}}(1395, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 2}\)