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Properties

Label 912.2.v
Level $912$
Weight $2$
Character orbit 912.v
Rep. character $\chi_{912}(419,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Newform subspaces $1$
Sturm bound $320$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(320\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 328 288 40
Cusp forms 312 288 24
Eisenstein series 16 0 16

Trace form

\( 288 q + 12 q^{6} + O(q^{10}) \) \( 288 q + 12 q^{6} + 12 q^{12} - 32 q^{16} - 20 q^{18} - 40 q^{22} - 36 q^{24} - 24 q^{27} - 24 q^{28} - 40 q^{30} + 32 q^{34} - 28 q^{36} - 48 q^{39} + 72 q^{40} - 20 q^{42} - 32 q^{43} + 52 q^{48} + 288 q^{49} - 40 q^{51} - 8 q^{52} + 56 q^{54} - 64 q^{55} - 72 q^{58} + 16 q^{60} - 72 q^{64} - 76 q^{66} - 64 q^{67} - 60 q^{72} - 116 q^{78} - 32 q^{82} - 20 q^{84} + 80 q^{88} - 8 q^{90} + 48 q^{91} - 48 q^{93} + 24 q^{94} - 16 q^{96} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.2.v.a 912.v 48.k $288$ $7.282$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)