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Properties

Label 1216.2.m
Level $1216$
Weight $2$
Character orbit 1216.m
Rep. character $\chi_{1216}(303,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $1$
Sturm bound $320$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(320\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 336 84 252
Cusp forms 304 76 228
Eisenstein series 32 8 24

Trace form

\( 76 q - 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93} - 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1216.2.m.a 1216.m 304.m $76$ $9.710$ None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$

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

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