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Properties

Label 1216.2.z
Level $1216$
Weight $2$
Character orbit 1216.z
Rep. character $\chi_{1216}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $152$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

Total New Old
Modular forms 672 168 504
Cusp forms 608 152 456
Eisenstein series 64 16 48

Trace form

\( 152 q + 2 q^{3} - 2 q^{5} + O(q^{10}) \) \( 152 q + 2 q^{3} - 2 q^{5} + 8 q^{11} - 2 q^{13} + 20 q^{15} - 4 q^{17} + 12 q^{19} + 4 q^{21} + 20 q^{27} - 2 q^{29} + 64 q^{31} - 4 q^{33} - 32 q^{35} - 8 q^{37} + 2 q^{43} - 16 q^{45} + 4 q^{47} - 120 q^{49} - 2 q^{51} - 2 q^{53} + 2 q^{59} + 30 q^{61} - 24 q^{63} - 16 q^{65} + 26 q^{67} - 84 q^{69} - 112 q^{75} + 48 q^{77} + 12 q^{79} + 40 q^{81} + 48 q^{83} + 34 q^{85} - 12 q^{91} - 8 q^{93} + 32 q^{95} - 4 q^{97} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

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