Space of modular forms of level 1710, weight 4, and Character 1710.cj

• Label: 1710.4.cj
• Level: $1710$
• Weight: $4$
• Character orbit: 1710.cj
• Rep. character: $\chi_{1710}(217,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $600$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1710.cj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1710, [\chi])\).

	Total	New	Old
Modular forms	4384	600	3784
Cusp forms	4256	600	3656
Eisenstein series	128	0	128

Trace form

600 * q - 16 * q^5 + 16 * q^7 + 56 * q^11 + 4800 * q^16 - 224 * q^17 - 432 * q^22 + 44 * q^23 - 152 * q^25 - 608 * q^26 - 32 * q^28 + 896 * q^35 + 200 * q^38 - 444 * q^41 + 208 * q^43 - 2352 * q^47 + 1872 * q^53 - 1480 * q^55 + 1728 * q^61 + 16 * q^62 - 2856 * q^67 + 1792 * q^68 + 3024 * q^70 + 1728 * q^73 + 608 * q^76 - 824 * q^77 + 256 * q^80 + 496 * q^82 - 568 * q^83 - 3572 * q^85 - 528 * q^86 + 7320 * q^91 - 176 * q^92 - 3596 * q^95 + 288 * q^97 + 528 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1710, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)