Properties

Label 59.7.b
Level $59$
Weight $7$
Character orbit 59.b
Rep. character $\chi_{59}(58,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $3$
Sturm bound $35$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(35\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(59, [\chi])\).

Total New Old
Modular forms 31 31 0
Cusp forms 29 29 0
Eisenstein series 2 2 0

Trace form

\( 29 q + 10 q^{3} - 898 q^{4} + 142 q^{5} + 406 q^{7} + 7619 q^{9} + O(q^{10}) \) \( 29 q + 10 q^{3} - 898 q^{4} + 142 q^{5} + 406 q^{7} + 7619 q^{9} - 1124 q^{12} + 540 q^{15} + 25022 q^{16} + 9042 q^{17} + 3850 q^{19} - 46896 q^{20} + 3700 q^{21} + 11238 q^{22} + 65667 q^{25} - 64590 q^{26} + 35980 q^{27} - 45542 q^{28} - 31730 q^{29} + 46276 q^{35} - 185298 q^{36} + 91914 q^{41} + 260794 q^{45} + 287148 q^{46} + 479572 q^{48} - 109953 q^{49} + 329932 q^{51} + 8238 q^{53} - 1296636 q^{57} - 289955 q^{59} - 1894352 q^{60} + 630140 q^{62} + 566818 q^{63} - 1013830 q^{64} - 869200 q^{66} + 842014 q^{68} - 286426 q^{71} - 2294090 q^{74} + 2800318 q^{75} + 247144 q^{76} - 375064 q^{78} + 4702 q^{79} + 1920984 q^{80} - 841623 q^{81} + 2367304 q^{84} + 864044 q^{85} + 5031110 q^{86} - 4790492 q^{87} + 725994 q^{88} + 2835768 q^{94} + 1047852 q^{95} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
59.7.b.a 59.b 59.b $1$ $13.573$ \(\Q\) \(\Q(\sqrt{-59}) \) 59.7.b.a \(0\) \(-5\) \(191\) \(155\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{3}+2^{6}q^{4}+191q^{5}+155q^{7}+\cdots\)
59.7.b.b 59.b 59.b $2$ $13.573$ \(\Q(\sqrt{177}) \) \(\Q(\sqrt{-59}) \) 59.7.b.b \(0\) \(5\) \(-191\) \(-155\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+7\beta )q^{3}+2^{6}q^{4}+(-85-21\beta )q^{5}+\cdots\)
59.7.b.c 59.b 59.b $26$ $13.573$ None 59.7.b.c \(0\) \(10\) \(142\) \(406\) $\mathrm{SU}(2)[C_{2}]$