Space of modular forms of level 1690, weight 2, and Character 1690.y

• Label: 1690.2.y
• Level: $1690$
• Weight: $2$
• Character orbit: 1690.y
• Rep. character: $\chi_{1690}(61,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $1488$
• Sturm bound: $546$

Defining parameters

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.y (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{39})\)
Sturm bound:			\(546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1690, [\chi])\).

	Total	New	Old
Modular forms	6624	1488	5136
Cusp forms	6432	1488	4944
Eisenstein series	192	0	192

Trace form

1488 * q + 62 * q^4 - 8 * q^7 + 70 * q^9 - 2 * q^10 - 2 * q^11 - 100 * q^13 - 4 * q^14 + 4 * q^15 + 62 * q^16 - 4 * q^17 - 16 * q^18 + 6 * q^19 + 24 * q^21 + 48 * q^22 + 8 * q^23 - 124 * q^25 - 8 * q^26 - 24 * q^27 - 8 * q^28 + 16 * q^29 - 4 * q^30 + 44 * q^31 + 20 * q^33 + 16 * q^34 - 2 * q^35 + 70 * q^36 + 12 * q^37 + 16 * q^38 - 28 * q^39 + 4 * q^40 - 4 * q^41 + 12 * q^42 + 16 * q^43 + 4 * q^44 - 16 * q^45 + 8 * q^46 - 280 * q^47 + 90 * q^49 - 24 * q^51 - 8 * q^52 + 24 * q^53 - 324 * q^54 + 4 * q^55 + 2 * q^56 + 92 * q^57 + 92 * q^58 - 8 * q^60 + 20 * q^61 - 4 * q^62 - 32 * q^63 - 124 * q^64 + 2 * q^65 - 56 * q^66 + 104 * q^67 - 4 * q^68 + 4 * q^69 - 272 * q^71 + 8 * q^72 - 56 * q^73 + 14 * q^74 + 32 * q^76 - 8 * q^77 + 20 * q^78 - 24 * q^79 + 102 * q^81 - 8 * q^82 - 12 * q^84 + 12 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 510 * q^89 + 20 * q^90 + 86 * q^91 - 16 * q^92 + 616 * q^93 + 66 * q^94 + 16 * q^95 - 4 * q^97 - 16 * q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1690, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1690, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1690, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)