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

• Label: 1617.2.bh
• Level: $1617$
• Weight: $2$
• Character orbit: 1617.bh
• Rep. character: $\chi_{1617}(100,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $1128$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.bh (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(448\)

Dimensions

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

	Total	New	Old
Modular forms	2736	1128	1608
Cusp forms	2640	1128	1512
Eisenstein series	96	0	96

Trace form

1128 * q - 2 * q^3 + 96 * q^4 - 2 * q^7 - 24 * q^8 + 94 * q^9 + 12 * q^10 - 4 * q^12 - 12 * q^13 + 4 * q^14 + 108 * q^16 + 6 * q^19 + 32 * q^20 + 8 * q^21 + 98 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 16 * q^29 + 16 * q^30 + 146 * q^31 + 212 * q^32 - 4 * q^33 + 144 * q^34 - 48 * q^35 - 192 * q^36 + 72 * q^37 - 12 * q^38 - 16 * q^39 + 124 * q^40 - 80 * q^41 - 68 * q^42 - 20 * q^43 + 64 * q^44 + 40 * q^46 - 28 * q^47 - 128 * q^48 - 22 * q^49 + 376 * q^50 - 160 * q^52 - 52 * q^53 + 32 * q^55 - 24 * q^56 - 12 * q^57 - 8 * q^58 - 80 * q^59 + 20 * q^60 - 22 * q^61 + 88 * q^62 + 12 * q^63 - 160 * q^64 - 8 * q^66 + 30 * q^67 - 36 * q^68 + 24 * q^69 + 116 * q^70 + 64 * q^71 + 96 * q^72 + 30 * q^73 - 6 * q^75 - 36 * q^76 - 4 * q^77 + 80 * q^78 + 10 * q^79 - 68 * q^80 + 94 * q^81 - 140 * q^82 - 192 * q^83 + 52 * q^84 + 40 * q^85 - 340 * q^86 + 12 * q^87 + 20 * q^89 - 24 * q^90 - 214 * q^91 - 144 * q^92 - 2 * q^93 - 452 * q^94 + 40 * q^95 + 20 * q^96 - 96 * q^97 + 72 * q^98

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

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)