Properties

Label 289.4.b
Level $289$
Weight $4$
Character orbit 289.b
Rep. character $\chi_{289}(288,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $6$
Sturm bound $102$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(102\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(289, [\chi])\).

Total New Old
Modular forms 86 74 12
Cusp forms 68 60 8
Eisenstein series 18 14 4

Trace form

\( 60 q + 2 q^{2} + 222 q^{4} + 18 q^{8} - 392 q^{9} + O(q^{10}) \) \( 60 q + 2 q^{2} + 222 q^{4} + 18 q^{8} - 392 q^{9} - 164 q^{13} - 12 q^{15} + 878 q^{16} - 290 q^{18} + 100 q^{19} - 144 q^{21} - 388 q^{25} + 492 q^{26} - 1202 q^{30} - 264 q^{32} + 1256 q^{33} - 1076 q^{35} - 536 q^{36} - 272 q^{38} + 882 q^{42} + 392 q^{43} - 1044 q^{47} - 1016 q^{49} + 1720 q^{50} - 932 q^{52} + 268 q^{53} - 252 q^{55} + 1032 q^{59} + 926 q^{60} - 1670 q^{64} - 1740 q^{66} + 244 q^{67} - 1688 q^{69} + 52 q^{70} + 1376 q^{72} + 188 q^{76} - 464 q^{77} + 2788 q^{81} + 2700 q^{83} - 2484 q^{84} + 3294 q^{86} - 40 q^{87} - 2120 q^{89} - 968 q^{93} - 540 q^{94} - 128 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(289, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
289.4.b.a 289.b 17.b $2$ $17.052$ \(\Q(\sqrt{-1}) \) None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{2}-4iq^{3}+q^{4}+3iq^{5}-12iq^{6}+\cdots\)
289.4.b.b 289.b 17.b $6$ $17.052$ 6.0.27793984.1 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(8-\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.b.c 289.b 17.b $8$ $17.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{2}-\beta _{4}q^{3}+(5-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
289.4.b.d 289.b 17.b $8$ $17.052$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(3-\beta _{2}+\cdots)q^{4}+\cdots\)
289.4.b.e 289.b 17.b $12$ $17.052$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{6})q^{2}+\beta _{11}q^{3}+(2+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
289.4.b.f 289.b 17.b $24$ $17.052$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(289, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(289, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)