↑

Properties

Label 1380.4.h
Level $1380$
Weight $4$
Character orbit 1380.h
Rep. character $\chi_{1380}(1151,\cdot)$
Character field $\Q$
Dimension $528$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1380.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1380, [\chi])\).

Total New Old
Modular forms 872 528 344
Cusp forms 856 528 328
Eisenstein series 16 0 16

Trace form

\( 528 q - 30 q^{6} - 40 q^{9} + O(q^{10}) \) \( 528 q - 30 q^{6} - 40 q^{9} + 298 q^{12} - 144 q^{13} - 326 q^{18} + 504 q^{22} + 868 q^{24} - 13200 q^{25} + 72 q^{28} + 80 q^{30} - 1696 q^{33} + 360 q^{34} - 302 q^{36} - 1008 q^{37} - 224 q^{42} - 1738 q^{48} - 23712 q^{49} - 180 q^{52} + 2108 q^{54} - 2832 q^{57} - 1188 q^{58} - 980 q^{60} - 2160 q^{61} + 1548 q^{64} + 2124 q^{66} - 1080 q^{70} - 2156 q^{72} + 4608 q^{73} - 2352 q^{76} - 1266 q^{78} - 4600 q^{81} - 3684 q^{82} + 2312 q^{84} + 1560 q^{88} + 2340 q^{90} + 4272 q^{93} + 1332 q^{94} + 942 q^{96} + 4896 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1380, [\chi]) \cong \)