Space of modular forms of level 1682, weight 2, and Character 1682.h

• Label: 1682.2.h
• Level: $1682$
• Weight: $2$
• Character orbit: 1682.h
• Rep. character: $\chi_{1682}(57,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $2016$
• Sturm bound: $435$

Defining parameters

Level:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1682.h (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 841 \)
Character field:			\(\Q(\zeta_{58})\)
Sturm bound:			\(435\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1682, [\chi])\).

	Total	New	Old
Modular forms	6160	2016	4144
Cusp forms	6048	2016	4032
Eisenstein series	112	0	112

Trace form

2016 * q + 72 * q^4 - 2 * q^5 + 2 * q^6 - 54 * q^7 + 66 * q^9 - 116 * q^11 + 2 * q^13 - 72 * q^16 + 174 * q^17 + 2 * q^20 - 10 * q^22 + 12 * q^23 - 2 * q^24 - 62 * q^25 - 58 * q^26 + 54 * q^28 - 10 * q^29 + 8 * q^30 - 16 * q^33 - 4 * q^34 + 178 * q^35 - 66 * q^36 + 2 * q^38 - 4 * q^42 - 56 * q^45 + 290 * q^47 - 6 * q^49 - 12 * q^51 - 2 * q^52 + 10 * q^53 + 16 * q^54 + 4 * q^58 + 98 * q^59 + 8 * q^62 + 72 * q^64 - 282 * q^65 - 116 * q^66 - 18 * q^67 + 58 * q^69 + 8 * q^71 + 18 * q^74 + 58 * q^76 + 4 * q^78 - 2 * q^80 - 64 * q^81 - 20 * q^82 - 142 * q^83 - 18 * q^86 + 4 * q^87 + 10 * q^88 + 116 * q^89 + 232 * q^90 + 170 * q^91 - 12 * q^92 - 4 * q^93 + 8 * q^94 + 2 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(1682, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1682, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1682, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(841, [\chi])\)\(^{\oplus 2}\)