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Properties

Label 16.4.e
Level $16$
Weight $4$
Character orbit 16.e
Rep. character $\chi_{16}(5,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(16, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} + O(q^{10}) \) \( 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20} + 52 q^{21} - 588 q^{22} - 848 q^{24} - 264 q^{26} + 184 q^{27} + 280 q^{28} - 202 q^{29} + 1236 q^{30} + 368 q^{31} + 968 q^{32} - 4 q^{33} + 436 q^{34} + 476 q^{35} - 596 q^{36} - 10 q^{37} - 1232 q^{38} - 1336 q^{40} - 680 q^{42} - 838 q^{43} + 868 q^{44} + 194 q^{45} + 1132 q^{46} - 944 q^{47} + 1768 q^{48} + 94 q^{49} + 726 q^{50} - 1500 q^{51} - 236 q^{52} - 378 q^{53} - 1376 q^{54} - 488 q^{56} + 8 q^{58} + 1706 q^{59} - 192 q^{60} + 910 q^{61} - 80 q^{62} + 2628 q^{63} + 512 q^{64} - 492 q^{65} - 428 q^{66} + 1942 q^{67} - 880 q^{68} + 580 q^{69} + 160 q^{70} + 1092 q^{72} - 452 q^{74} - 2954 q^{75} - 1228 q^{76} - 268 q^{77} - 772 q^{78} - 4416 q^{79} - 2648 q^{80} + 482 q^{81} - 704 q^{82} - 2562 q^{83} + 1960 q^{84} - 12 q^{85} + 3764 q^{86} + 1528 q^{88} + 1896 q^{90} + 3332 q^{91} + 632 q^{92} - 2192 q^{93} - 3248 q^{94} + 6900 q^{95} - 4432 q^{96} - 4 q^{97} + 314 q^{98} + 4958 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(16, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.4.e.a 16.e 16.e $10$ $0.944$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)