↑

Properties

Label 1224.4.bj
Level $1224$
Weight $4$
Character orbit 1224.bj
Rep. character $\chi_{1224}(205,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1152$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1224.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

Total New Old
Modular forms 1304 1152 152
Cusp forms 1288 1152 136
Eisenstein series 16 0 16

Trace form

\( 1152 q + 30 q^{6} + 12 q^{8} + O(q^{10}) \) \( 1152 q + 30 q^{6} + 12 q^{8} + 156 q^{12} + 662 q^{18} - 154 q^{20} - 552 q^{23} + 382 q^{24} + 14400 q^{25} - 776 q^{26} + 184 q^{30} + 230 q^{32} + 1208 q^{36} - 624 q^{38} - 600 q^{39} - 702 q^{42} - 828 q^{44} + 562 q^{48} - 28224 q^{49} + 620 q^{50} + 918 q^{52} - 1786 q^{54} + 316 q^{56} - 594 q^{58} + 674 q^{60} - 284 q^{62} + 540 q^{64} + 1720 q^{66} + 7952 q^{71} + 2048 q^{72} - 1722 q^{74} + 3480 q^{78} - 10036 q^{80} - 1232 q^{81} - 1404 q^{82} - 4768 q^{84} + 4162 q^{86} - 6824 q^{87} + 2088 q^{88} + 1696 q^{89} - 4790 q^{90} - 2660 q^{92} - 3006 q^{94} + 6080 q^{95} - 2838 q^{96} + 8172 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)