↑

Properties

Label 1425.2.k
Level $1425$
Weight $2$
Character orbit 1425.k
Rep. character $\chi_{1425}(818,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $400$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

Total New Old
Modular forms 424 216 208
Cusp forms 376 216 160
Eisenstein series 48 0 48

Trace form

\( 216 q + 4 q^{3} + 16 q^{6} + 8 q^{7} + O(q^{10}) \) \( 216 q + 4 q^{3} + 16 q^{6} + 8 q^{7} - 16 q^{12} + 16 q^{13} - 216 q^{16} + 16 q^{21} - 24 q^{22} - 8 q^{27} - 8 q^{28} - 32 q^{31} + 16 q^{33} - 16 q^{36} + 24 q^{37} + 64 q^{42} + 16 q^{43} - 64 q^{46} + 12 q^{48} - 48 q^{51} - 72 q^{52} + 72 q^{58} + 128 q^{61} + 8 q^{63} - 80 q^{66} + 56 q^{67} + 20 q^{72} - 40 q^{73} - 16 q^{78} + 168 q^{81} + 88 q^{82} - 168 q^{88} + 64 q^{91} + 8 q^{93} + 96 q^{96} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)