Properties

Label 23.10.c
Level $23$
Weight $10$
Character orbit 23.c
Rep. character $\chi_{23}(2,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $170$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 23.c (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(23, [\chi])\).

Total New Old
Modular forms 190 190 0
Cusp forms 170 170 0
Eisenstein series 20 20 0

Trace form

\( 170 q - 43 q^{2} - 157 q^{3} - 4619 q^{4} + 2265 q^{5} + 1532 q^{6} + 8605 q^{7} - 28412 q^{8} - 84756 q^{9} + O(q^{10}) \) \( 170 q - 43 q^{2} - 157 q^{3} - 4619 q^{4} + 2265 q^{5} + 1532 q^{6} + 8605 q^{7} - 28412 q^{8} - 84756 q^{9} - 1485 q^{10} + 81163 q^{11} - 60588 q^{12} - 11089 q^{13} + 67821 q^{14} + 621703 q^{15} - 1909531 q^{16} - 753661 q^{17} - 726672 q^{18} + 2352257 q^{19} + 6591465 q^{20} - 5684355 q^{21} - 5946642 q^{22} - 4490346 q^{23} + 4177174 q^{24} + 545458 q^{25} + 10422936 q^{26} - 1144735 q^{27} - 5527093 q^{28} - 7002529 q^{29} - 24506121 q^{30} + 11263929 q^{31} + 46016973 q^{32} - 1003951 q^{33} - 12993751 q^{34} + 68486143 q^{35} - 39331073 q^{36} - 89526363 q^{37} - 94102532 q^{38} + 49805983 q^{39} + 272326679 q^{40} + 52330165 q^{41} + 66250835 q^{42} - 21814465 q^{43} - 105726610 q^{44} - 198216616 q^{45} - 320080243 q^{46} - 153217032 q^{47} + 325997510 q^{48} + 195154842 q^{49} + 365787994 q^{50} + 174282061 q^{51} - 10096756 q^{52} - 224456041 q^{53} - 1140098178 q^{54} - 379496843 q^{55} + 389457460 q^{56} + 84964017 q^{57} + 547323529 q^{58} + 129076539 q^{59} - 1362120205 q^{60} + 447029913 q^{61} + 796216240 q^{62} + 1061159027 q^{63} + 922158762 q^{64} - 180608527 q^{65} + 277416862 q^{66} - 319825461 q^{67} - 2693182722 q^{68} - 1160581515 q^{69} - 452062394 q^{70} + 97280089 q^{71} + 437472589 q^{72} + 839365275 q^{73} + 1826280178 q^{74} + 2985570317 q^{75} + 6472764418 q^{76} - 338423227 q^{77} - 4686899840 q^{78} - 4912832511 q^{79} - 7619127772 q^{80} - 5223670776 q^{81} + 1981501322 q^{82} + 806964537 q^{83} + 10896222429 q^{84} + 6493376823 q^{85} + 1571113345 q^{86} + 3874701515 q^{87} - 1784251567 q^{88} - 1388933039 q^{89} - 7300929742 q^{90} - 3850658378 q^{91} - 6763730354 q^{92} - 4102556922 q^{93} + 62806987 q^{94} - 5662987785 q^{95} + 19038690045 q^{96} + 10282527577 q^{97} + 6376122113 q^{98} + 11619425557 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.10.c.a 23.c 23.c $170$ $11.846$ None \(-43\) \(-157\) \(2265\) \(8605\) $\mathrm{SU}(2)[C_{11}]$