Properties

Label 1470.2.bb
Level $1470$
Weight $2$
Character orbit 1470.bb
Rep. character $\chi_{1470}(169,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
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.bb (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2064 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336q + 56q^{4} + 8q^{5} - 4q^{6} + 56q^{9} + O(q^{10}) \) \( 336q + 56q^{4} + 8q^{5} - 4q^{6} + 56q^{9} + 4q^{10} + 48q^{11} - 4q^{14} - 10q^{15} - 56q^{16} - 72q^{19} + 20q^{20} + 8q^{21} + 4q^{24} + 4q^{25} - 20q^{26} - 16q^{29} + 24q^{31} + 16q^{34} + 4q^{35} - 56q^{36} + 40q^{39} + 10q^{40} - 80q^{41} + 36q^{44} + 20q^{45} + 8q^{46} + 40q^{49} - 16q^{50} - 40q^{51} + 4q^{54} - 34q^{55} - 24q^{56} + 92q^{59} + 10q^{60} - 64q^{61} + 56q^{64} + 48q^{65} - 16q^{66} - 10q^{70} + 16q^{71} + 20q^{74} + 16q^{75} + 16q^{76} - 24q^{79} + 8q^{80} - 56q^{81} - 8q^{84} + 64q^{85} + 120q^{86} - 40q^{89} - 4q^{90} - 44q^{91} + 84q^{94} + 88q^{95} - 4q^{96} + 8q^{99} + O(q^{100}) \)

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

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