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Properties

Label 4.5.b
Level $4$
Weight $5$
Character orbit 4.b
Rep. character $\chi_{4}(3,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(4, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 4 q^{2} + 16 q^{4} - 14 q^{5} - 64 q^{8} + 81 q^{9} + O(q^{10}) \) \( q - 4 q^{2} + 16 q^{4} - 14 q^{5} - 64 q^{8} + 81 q^{9} + 56 q^{10} - 238 q^{13} + 256 q^{16} + 322 q^{17} - 324 q^{18} - 224 q^{20} - 429 q^{25} + 952 q^{26} + 82 q^{29} - 1024 q^{32} - 1288 q^{34} + 1296 q^{36} + 2162 q^{37} + 896 q^{40} - 3038 q^{41} - 1134 q^{45} + 2401 q^{49} + 1716 q^{50} - 3808 q^{52} + 2482 q^{53} - 328 q^{58} - 6958 q^{61} + 4096 q^{64} + 3332 q^{65} + 5152 q^{68} - 5184 q^{72} + 1442 q^{73} - 8648 q^{74} - 3584 q^{80} + 6561 q^{81} + 12152 q^{82} - 4508 q^{85} - 9758 q^{89} + 4536 q^{90} - 1918 q^{97} - 9604 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.5.b.a 4.b 4.b $1$ $0.413$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(-14\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)