Space of modular forms of level 1617, weight 2, and Character 1617.bj

• Label: 1617.2.bj
• Level: $1617$
• Weight: $2$
• Character orbit: 1617.bj
• Rep. character: $\chi_{1617}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $640$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.bj (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1617, [\chi])\).

	Total	New	Old
Modular forms	1920	640	1280
Cusp forms	1664	640	1024
Eisenstein series	256	0	256

Trace form

640 * q - 88 * q^4 - 12 * q^5 + 80 * q^8 - 80 * q^9 - 2 * q^11 - 12 * q^15 + 40 * q^16 + 60 * q^17 + 20 * q^18 - 60 * q^22 + 32 * q^23 + 90 * q^24 - 64 * q^25 - 24 * q^26 - 40 * q^29 + 18 * q^31 - 18 * q^33 - 176 * q^36 + 24 * q^37 + 24 * q^38 + 90 * q^40 + 144 * q^44 - 12 * q^45 - 140 * q^46 + 24 * q^47 + 20 * q^51 - 28 * q^53 + 54 * q^58 - 48 * q^59 - 12 * q^60 - 30 * q^61 + 256 * q^64 - 36 * q^66 + 64 * q^67 - 180 * q^68 + 8 * q^71 - 20 * q^72 - 90 * q^73 - 40 * q^74 + 24 * q^75 + 168 * q^78 - 70 * q^79 - 228 * q^80 + 80 * q^81 - 168 * q^82 + 60 * q^85 + 72 * q^86 - 92 * q^88 - 344 * q^92 - 80 * q^93 - 10 * q^95 + 76 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)