Space of modular forms of level 1470, weight 4, and Character 1470.g

• Label: 1470.4.g
• Level: $1470$
• Weight: $4$
• Character orbit: 1470.g
• Rep. character: $\chi_{1470}(589,\cdot)$
• Character field: $\Q$
• Dimension: $122$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1470, [\chi])\).

	Total	New	Old
Modular forms	1040	122	918
Cusp forms	976	122	854
Eisenstein series	64	0	64

Trace form

122 * q - 488 * q^4 - 28 * q^5 + 12 * q^6 - 1098 * q^9 - 20 * q^10 - 140 * q^11 + 18 * q^15 + 1952 * q^16 - 48 * q^19 + 112 * q^20 - 48 * q^24 + 482 * q^25 + 520 * q^26 - 112 * q^29 + 24 * q^30 - 200 * q^31 - 456 * q^34 + 4392 * q^36 - 348 * q^39 + 80 * q^40 + 188 * q^41 + 560 * q^44 + 252 * q^45 - 480 * q^46 - 1504 * q^50 - 540 * q^51 - 108 * q^54 + 1008 * q^55 - 36 * q^59 - 72 * q^60 - 724 * q^61 - 7808 * q^64 - 2380 * q^65 + 216 * q^66 - 1896 * q^69 + 2360 * q^71 - 760 * q^74 - 888 * q^75 + 192 * q^76 + 4280 * q^79 - 448 * q^80 + 9882 * q^81 + 1044 * q^85 + 144 * q^86 + 3836 * q^89 + 180 * q^90 - 912 * q^94 + 1408 * q^95 + 192 * q^96 + 1260 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1470, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)