↑

Properties

Label 1428.2.c
Level $1428$
Weight $2$
Character orbit 1428.c
Rep. character $\chi_{1428}(307,\cdot)$
Character field $\Q$
Dimension $128$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 296 128 168
Cusp forms 280 128 152
Eisenstein series 16 0 16

Trace form

\( 128 q + 4 q^{2} - 4 q^{4} + 28 q^{8} + 128 q^{9} + O(q^{10}) \) \( 128 q + 4 q^{2} - 4 q^{4} + 28 q^{8} + 128 q^{9} - 12 q^{14} - 4 q^{16} + 4 q^{18} + 8 q^{21} - 112 q^{25} - 12 q^{28} + 32 q^{29} + 4 q^{32} - 4 q^{36} + 48 q^{37} + 20 q^{42} - 24 q^{44} + 64 q^{46} - 32 q^{49} - 76 q^{50} - 32 q^{53} + 36 q^{56} + 48 q^{57} + 16 q^{58} + 16 q^{60} - 4 q^{64} - 32 q^{65} + 16 q^{70} + 28 q^{72} - 32 q^{74} + 24 q^{78} + 128 q^{81} - 12 q^{84} + 32 q^{86} - 32 q^{88} + 56 q^{92} - 16 q^{93} + 4 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)