↑

Properties

Label 2448.2.fe
Level $2448$
Weight $2$
Character orbit 2448.fe
Rep. character $\chi_{2448}(65,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1696$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2448.fe (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2448, [\chi])\).

Total New Old
Modular forms 7104 1760 5344
Cusp forms 6720 1696 5024
Eisenstein series 384 64 320

Trace form

\( 1696 q + 16 q^{3} - 24 q^{5} + 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 1696 q + 16 q^{3} - 24 q^{5} + 8 q^{7} - 16 q^{9} + 24 q^{11} - 8 q^{13} + 16 q^{15} + 32 q^{19} - 16 q^{21} + 24 q^{23} - 8 q^{25} + 16 q^{27} - 24 q^{29} + 8 q^{31} - 32 q^{37} + 16 q^{39} - 24 q^{41} + 8 q^{43} - 16 q^{45} + 24 q^{47} - 8 q^{49} + 16 q^{51} + 32 q^{55} - 32 q^{57} + 24 q^{59} - 8 q^{61} - 128 q^{63} - 24 q^{65} - 160 q^{69} - 32 q^{73} - 128 q^{75} - 24 q^{77} + 8 q^{79} - 32 q^{81} + 24 q^{83} - 8 q^{85} + 16 q^{87} + 32 q^{91} - 16 q^{93} + 24 q^{95} - 8 q^{97} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1224, [\chi])\)\(^{\oplus 2}\)