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

• Label: 1617.2.j
• Level: $1617$
• Weight: $2$
• Character orbit: 1617.j
• Rep. character: $\chi_{1617}(148,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $328$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(448\)

Dimensions

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

	Total	New	Old
Modular forms	960	328	632
Cusp forms	832	328	504
Eisenstein series	128	0	128

Trace form

328 * q + 4 * q^2 - 78 * q^4 + 4 * q^5 + 2 * q^6 - 8 * q^8 - 82 * q^9 - 20 * q^10 + 18 * q^11 - 8 * q^12 + 6 * q^13 - 10 * q^15 - 70 * q^16 - 22 * q^17 - 6 * q^18 + 12 * q^19 + 54 * q^20 - 24 * q^22 + 36 * q^23 - 12 * q^24 - 72 * q^25 + 42 * q^26 + 4 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^32 + 2 * q^33 - 64 * q^34 - 78 * q^36 + 6 * q^37 + 6 * q^38 - 16 * q^39 - 8 * q^40 - 28 * q^41 + 40 * q^43 - 98 * q^44 + 4 * q^45 - 34 * q^46 - 6 * q^47 + 8 * q^48 + 74 * q^50 - 24 * q^51 + 58 * q^52 + 18 * q^53 - 8 * q^54 - 16 * q^55 + 16 * q^57 - 8 * q^58 + 30 * q^59 + 48 * q^60 + 18 * q^61 - 4 * q^62 - 42 * q^64 + 4 * q^65 + 12 * q^66 - 52 * q^67 - 60 * q^68 + 18 * q^69 - 28 * q^71 + 2 * q^72 - 28 * q^73 + 90 * q^74 + 24 * q^75 - 24 * q^76 - 56 * q^78 - 42 * q^79 - 198 * q^80 - 82 * q^81 + 10 * q^82 + 54 * q^83 - 38 * q^85 + 164 * q^86 - 64 * q^87 - 102 * q^88 + 68 * q^89 + 20 * q^90 + 206 * q^92 - 36 * q^93 + 2 * q^94 + 114 * q^95 + 68 * q^96 + 2 * q^97 - 12 * 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

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)