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

• Label: 1617.2.bg
• Level: $1617$
• Weight: $2$
• Character orbit: 1617.bg
• Rep. character: $\chi_{1617}(214,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $640$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.bg (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
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 - 8 * q^2 + 72 * q^4 + 4 * q^5 + 8 * q^6 - 32 * q^8 + 80 * q^9 + 36 * q^10 - 2 * q^11 + 16 * q^13 + 12 * q^15 + 104 * q^16 + 12 * q^18 - 8 * q^19 - 48 * q^20 + 68 * q^22 - 30 * q^24 + 120 * q^25 - 8 * q^26 + 88 * q^29 - 16 * q^30 - 6 * q^31 - 16 * q^32 + 6 * q^33 + 144 * q^34 - 144 * q^36 + 48 * q^37 + 8 * q^38 - 42 * q^40 + 48 * q^41 + 24 * q^43 + 72 * q^44 + 4 * q^45 + 68 * q^46 + 44 * q^47 + 112 * q^50 - 12 * q^51 - 12 * q^52 + 76 * q^53 + 16 * q^54 + 56 * q^55 + 32 * q^57 - 22 * q^58 - 8 * q^59 - 12 * q^60 + 18 * q^61 - 96 * q^62 - 48 * q^64 - 32 * q^65 + 12 * q^66 - 96 * q^67 + 56 * q^68 - 24 * q^69 - 200 * q^71 - 4 * q^72 + 6 * q^73 - 36 * q^74 + 8 * q^75 - 272 * q^76 - 216 * q^78 + 18 * q^79 + 88 * q^80 + 80 * q^81 - 128 * q^83 - 276 * q^85 - 240 * q^86 + 100 * q^87 + 52 * q^88 - 72 * q^89 + 8 * q^90 + 152 * q^92 + 80 * q^93 + 52 * q^94 - 6 * q^95 - 4 * q^96 - 32 * q^97 - 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

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