Space of modular forms of level 1290, weight 2, and Character 1290.j

• Label: 1290.2.j
• Level: $1290$
• Weight: $2$
• Character orbit: 1290.j
• Rep. character: $\chi_{1290}(173,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $168$
• Sturm bound: $528$

Defining parameters

Level:	\( N \)	\(=\)	\( 1290 = 2 \cdot 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1290.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1290, [\chi])\).

	Total	New	Old
Modular forms	544	168	376
Cusp forms	512	168	344
Eisenstein series	32	0	32

Trace form

168 * q + 8 * q^3 + 8 * q^7 - 8 * q^10 - 8 * q^12 + 16 * q^13 - 16 * q^15 - 168 * q^16 - 16 * q^18 - 16 * q^21 + 8 * q^22 + 32 * q^25 + 32 * q^27 + 8 * q^28 - 8 * q^33 + 16 * q^36 - 48 * q^37 - 16 * q^40 - 32 * q^42 + 56 * q^45 - 8 * q^48 - 16 * q^52 - 8 * q^55 - 8 * q^57 + 40 * q^58 + 8 * q^60 + 32 * q^61 + 48 * q^63 + 48 * q^67 - 8 * q^70 + 16 * q^72 - 24 * q^73 - 72 * q^75 - 24 * q^78 - 64 * q^81 + 32 * q^82 - 16 * q^85 + 20 * q^87 + 8 * q^88 - 12 * q^90 - 56 * q^93 - 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1290, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1290, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1290, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(645, [\chi])\)\(^{\oplus 2}\)