↑

Properties

Label 1216.4.bu
Level $1216$
Weight $4$
Character orbit 1216.bu
Rep. character $\chi_{1216}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1416$
Sturm bound $640$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.bu (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1216, [\chi])\).

Total New Old
Modular forms 5856 1464 4392
Cusp forms 5664 1416 4248
Eisenstein series 192 48 144

Trace form

\( 1416 q + 12 q^{3} - 12 q^{5} + O(q^{10}) \) \( 1416 q + 12 q^{3} - 12 q^{5} + 6 q^{11} - 12 q^{13} + 24 q^{15} - 24 q^{17} + 12 q^{19} - 174 q^{21} + 6 q^{27} - 12 q^{29} + 2244 q^{31} - 24 q^{33} + 762 q^{35} - 24 q^{37} + 12 q^{43} - 6 q^{45} + 24 q^{47} + 31152 q^{49} - 2220 q^{51} - 12 q^{53} + 12 q^{59} - 12 q^{61} + 4140 q^{63} - 12 q^{65} + 12 q^{67} + 1578 q^{69} - 9888 q^{75} - 4140 q^{77} + 24 q^{79} - 24 q^{81} + 6 q^{83} + 1428 q^{85} + 2070 q^{91} + 150 q^{93} + 24 q^{95} - 24 q^{97} + 4386 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)