Space of modular forms of level 1870, weight 4, and Character 1870.q

• Label: 1870.4.q
• Level: $1870$
• Weight: $4$
• Character orbit: 1870.q
• Rep. character: $\chi_{1870}(1101,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $360$
• Sturm bound: $1296$

Defining parameters

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1870, [\chi])\).

	Total	New	Old
Modular forms	1960	360	1600
Cusp forms	1928	360	1568
Eisenstein series	32	0	32

Trace form

360 * q - 1440 * q^4 + 5760 * q^16 - 256 * q^17 - 32 * q^23 + 768 * q^29 + 352 * q^31 - 528 * q^33 + 480 * q^34 + 368 * q^37 + 1824 * q^38 + 464 * q^39 + 1152 * q^41 - 640 * q^45 - 960 * q^46 + 736 * q^47 - 3200 * q^51 + 2880 * q^54 + 4016 * q^57 + 864 * q^58 - 1248 * q^62 + 880 * q^63 - 23040 * q^64 - 2960 * q^67 + 1024 * q^68 - 3328 * q^69 + 2400 * q^71 - 2432 * q^73 - 2432 * q^74 - 5536 * q^78 - 688 * q^79 - 24040 * q^81 - 1824 * q^82 - 2240 * q^85 + 3200 * q^86 - 2400 * q^89 + 736 * q^91 + 128 * q^92 + 6320 * q^95 - 5136 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1870, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)