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Properties

Label 1470.2.bu
Level $1470$
Weight $2$
Character orbit 1470.bu
Rep. character $\chi_{1470}(73,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $1344$
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.bu (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 8256 1344 6912
Cusp forms 7872 1344 6528
Eisenstein series 384 0 384

Trace form

\( 1344 q - 24 q^{5} + 12 q^{7} + O(q^{10}) \) \( 1344 q - 24 q^{5} + 12 q^{7} - 12 q^{10} - 8 q^{11} + 20 q^{15} - 112 q^{16} + 56 q^{17} - 16 q^{21} - 20 q^{22} - 8 q^{23} + 8 q^{25} - 32 q^{26} + 12 q^{28} + 48 q^{31} - 12 q^{33} + 40 q^{35} + 224 q^{36} + 24 q^{37} + 48 q^{38} + 224 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{46} - 144 q^{47} + 208 q^{51} + 168 q^{55} + 96 q^{56} - 32 q^{58} + 176 q^{61} + 16 q^{67} - 8 q^{70} + 32 q^{71} + 24 q^{73} + 48 q^{75} - 80 q^{78} - 24 q^{80} - 112 q^{81} - 48 q^{82} + 224 q^{83} + 32 q^{85} - 88 q^{87} + 4 q^{88} + 40 q^{91} + 16 q^{92} - 8 q^{95} - 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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