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Properties

Label 23.19.b
Level $23$
Weight $19$
Character orbit 23.b
Rep. character $\chi_{23}(22,\cdot)$
Character field $\Q$
Dimension $35$
Newform subspaces $3$
Sturm bound $38$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(38\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(23, [\chi])\).

Total New Old
Modular forms 37 37 0
Cusp forms 35 35 0
Eisenstein series 2 2 0

Trace form

\( 35 q + 168 q^{2} - 20130 q^{3} + 4092072 q^{4} + 2318115 q^{6} + 18825195 q^{8} + 4214797041 q^{9} + O(q^{10}) \) \( 35 q + 168 q^{2} - 20130 q^{3} + 4092072 q^{4} + 2318115 q^{6} + 18825195 q^{8} + 4214797041 q^{9} - 5321755797 q^{12} - 655768946 q^{13} + 365919226384 q^{16} + 450489495579 q^{18} + 874880797443 q^{23} + 3021614025360 q^{24} - 3292642113085 q^{25} - 8213187707757 q^{26} - 7982123901036 q^{27} - 30667383347322 q^{29} + 61916976271654 q^{31} + 63545537188608 q^{32} - 97946624844120 q^{35} + 43210700594931 q^{36} + 111220720631940 q^{39} - 1087883639418714 q^{41} - 117414370775936 q^{46} - 770876632573578 q^{47} + 5112458972709003 q^{48} - 887909137819669 q^{49} + 3736249695919320 q^{50} - 2679946447733133 q^{52} - 3496693109910885 q^{54} - 8166714828852600 q^{55} - 18542223059304901 q^{58} - 14548975815379986 q^{59} + 5362886014107123 q^{62} + 22809068034472883 q^{64} - 64256080760341770 q^{69} + 46870559804852640 q^{70} + 31512883516333086 q^{71} + 136174746487938147 q^{72} + 58247715757776334 q^{73} - 89535755592176010 q^{75} + 250183815829725672 q^{77} - 564072937379856909 q^{78} + 25788506735558295 q^{81} - 501607580940050485 q^{82} + 490071094606517400 q^{85} - 194505376026720996 q^{87} - 1563136944458675832 q^{92} + 1843523091987505836 q^{93} + 1150778310490311179 q^{94} - 621924523779350640 q^{95} + 2865042234791107035 q^{96} - 1959791456322602664 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.19.b.a 23.b 23.b $1$ $47.239$ \(\Q\) \(\Q(\sqrt{-23}) \) 23.19.b.a \(1001\) \(28234\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+1001q^{2}+28234q^{3}+739857q^{4}+\cdots\)
23.19.b.b 23.b 23.b $2$ $47.239$ \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) 23.19.b.b \(-1001\) \(-28234\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-505-9\beta )q^{2}+(-14689-1144\beta )q^{3}+\cdots\)
23.19.b.c 23.b 23.b $32$ $47.239$ None 23.19.b.c \(168\) \(-20130\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$