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Properties

Label 1470.2.bi
Level $1470$
Weight $2$
Character orbit 1470.bi
Rep. character $\chi_{1470}(13,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $672$
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.bi (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4128 672 3456
Cusp forms 3936 672 3264
Eisenstein series 192 0 192

Trace form

\( 672 q - 12 q^{7} + O(q^{10}) \) \( 672 q - 12 q^{7} - 16 q^{11} - 20 q^{15} + 112 q^{16} - 56 q^{17} + 16 q^{21} + 20 q^{22} - 16 q^{23} + 16 q^{25} + 56 q^{26} + 12 q^{28} + 32 q^{35} + 112 q^{36} + 48 q^{37} + 112 q^{41} + 4 q^{42} - 16 q^{43} + 16 q^{46} + 168 q^{47} + 80 q^{51} - 168 q^{55} + 48 q^{56} + 20 q^{58} + 112 q^{61} + 12 q^{63} + 32 q^{67} - 64 q^{70} - 32 q^{71} + 80 q^{78} + 112 q^{81} + 112 q^{83} - 32 q^{85} + 28 q^{87} + 8 q^{88} - 40 q^{91} - 16 q^{92} - 16 q^{95} + 16 q^{98} + O(q^{100}) \)

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

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