↑

Properties

Label 1428.2.cj
Level $1428$
Weight $2$
Character orbit 1428.cj
Rep. character $\chi_{1428}(167,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2240$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1428.cj (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1428 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

Total New Old
Modular forms 2368 2368 0
Cusp forms 2240 2240 0
Eisenstein series 128 128 0

Trace form

\( 2240 q - 32 q^{4} - 32 q^{9} + O(q^{10}) \) \( 2240 q - 32 q^{4} - 32 q^{9} - 32 q^{18} - 16 q^{21} - 32 q^{22} - 64 q^{25} - 64 q^{28} - 16 q^{30} - 16 q^{36} - 64 q^{37} - 8 q^{42} - 32 q^{46} - 32 q^{49} - 32 q^{57} - 32 q^{58} - 16 q^{60} - 32 q^{64} - 48 q^{70} - 16 q^{72} - 16 q^{78} - 32 q^{81} - 64 q^{85} - 32 q^{88} - 32 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) into newform subspaces

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