↑

Properties

Label 780.4.ct
Level $780$
Weight $4$
Character orbit 780.ct
Rep. character $\chi_{780}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 780.ct (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(780, [\chi])\).

Total New Old
Modular forms 2064 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336 q + O(q^{10}) \) \( 336 q + 88 q^{15} - 96 q^{19} + 112 q^{21} - 504 q^{31} + 552 q^{39} - 132 q^{45} + 1728 q^{49} + 312 q^{55} + 528 q^{61} - 3696 q^{69} + 5640 q^{75} + 1200 q^{79} - 688 q^{81} - 2232 q^{85} - 1296 q^{91} - 248 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(780, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(780, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(780, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)