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

• Label: 1470.4.u
• Level: $1470$
• Weight: $4$
• Character orbit: 1470.u
• Rep. character: $\chi_{1470}(211,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $672$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1470.u (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	6096	672	5424
Cusp forms	6000	672	5328
Eisenstein series	96	0	96

Trace form

672 * q - 12 * q^3 - 448 * q^4 - 28 * q^7 - 1008 * q^9 + 40 * q^10 + 56 * q^11 - 48 * q^12 + 72 * q^14 - 1792 * q^16 + 16 * q^17 - 288 * q^19 - 84 * q^21 - 224 * q^22 - 2800 * q^25 + 760 * q^26 - 108 * q^27 - 112 * q^28 - 112 * q^29 + 104 * q^31 + 264 * q^33 + 480 * q^34 + 1640 * q^35 - 4032 * q^36 - 364 * q^37 + 2480 * q^38 - 420 * q^39 + 160 * q^40 + 616 * q^41 - 288 * q^42 - 56 * q^43 - 560 * q^44 - 784 * q^46 - 3680 * q^47 + 1152 * q^48 - 2944 * q^49 - 1680 * q^51 + 1456 * q^52 - 1456 * q^53 + 480 * q^55 + 512 * q^56 - 840 * q^57 + 1680 * q^58 + 5540 * q^59 + 1812 * q^61 + 5360 * q^62 + 1512 * q^63 - 7168 * q^64 - 280 * q^65 - 1848 * q^67 + 64 * q^68 - 1392 * q^69 + 1792 * q^71 - 7096 * q^73 + 5880 * q^74 - 300 * q^75 - 1152 * q^76 - 7008 * q^77 + 616 * q^79 - 9072 * q^81 + 960 * q^82 - 2800 * q^83 - 336 * q^84 - 2240 * q^85 + 2240 * q^86 + 2240 * q^88 - 7400 * q^89 + 360 * q^90 - 6660 * q^91 - 168 * q^93 - 5240 * q^94 + 2240 * q^95 - 9560 * q^97 + 2016 * q^98 + 504 * 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

\( S_{4}^{\mathrm{old}}(1470, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)