↑

Properties

Label 1216.3.l
Level $1216$
Weight $3$
Character orbit 1216.l
Rep. character $\chi_{1216}(495,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1216, [\chi])\).

Total New Old
Modular forms 656 144 512
Cusp forms 624 144 480
Eisenstein series 32 0 32

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 32 q^{11} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 224 q^{43} + 1008 q^{49} + 160 q^{51} - 160 q^{53} + 512 q^{55} + 416 q^{59} - 32 q^{65} - 160 q^{67} - 512 q^{71} - 384 q^{75} + 224 q^{77} - 1296 q^{81} + 480 q^{83} + 576 q^{91} + 96 q^{93} - 608 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)