Properties

Label 1470.2.u
Level $1470$
Weight $2$
Character orbit 1470.u
Rep. character $\chi_{1470}(211,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $240$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 2064 240 1824
Cusp forms 1968 240 1728
Eisenstein series 96 0 96

Trace form

\( 240q - 4q^{3} - 40q^{4} - 4q^{7} - 40q^{9} + O(q^{10}) \) \( 240q - 4q^{3} - 40q^{4} - 4q^{7} - 40q^{9} - 4q^{10} - 8q^{11} - 4q^{12} - 16q^{13} - 12q^{14} - 40q^{16} - 16q^{17} - 16q^{19} - 4q^{21} - 16q^{22} - 40q^{25} + 20q^{26} - 4q^{27} - 4q^{28} - 32q^{29} - 24q^{31} - 8q^{33} - 16q^{34} + 16q^{35} - 40q^{36} + 44q^{37} + 40q^{38} + 60q^{39} - 4q^{40} + 32q^{41} + 48q^{42} - 24q^{43} + 20q^{44} - 8q^{46} + 80q^{47} + 24q^{48} + 40q^{51} + 12q^{52} + 64q^{53} - 16q^{55} + 16q^{56} - 24q^{57} + 40q^{58} + 28q^{59} - 12q^{61} + 40q^{62} + 24q^{63} - 40q^{64} - 8q^{65} - 56q^{67} - 16q^{68} - 32q^{69} - 64q^{71} + 96q^{73} - 12q^{74} - 4q^{75} - 16q^{76} + 72q^{77} - 88q^{79} - 40q^{81} - 64q^{82} + 40q^{83} - 4q^{84} - 16q^{85} - 32q^{86} + 40q^{88} + 128q^{89} - 4q^{90} + 44q^{91} - 56q^{93} + 4q^{94} - 32q^{95} - 8q^{97} - 48q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

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