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Properties

Label 23.4.a
Level $23$
Weight $4$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(23))\).

Total New Old
Modular forms 7 5 2
Cusp forms 5 5 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(23\)Dim.
\(+\)\(4\)
\(-\)\(1\)

Trace form

\( 5 q + 2 q^{3} + 16 q^{4} + 8 q^{5} - 7 q^{6} + 8 q^{7} - 39 q^{8} - 35 q^{9} + O(q^{10}) \) \( 5 q + 2 q^{3} + 16 q^{4} + 8 q^{5} - 7 q^{6} + 8 q^{7} - 39 q^{8} - 35 q^{9} - 58 q^{10} + 42 q^{11} - 47 q^{12} + 54 q^{13} - 128 q^{14} + 40 q^{15} + 48 q^{16} + 18 q^{17} + 53 q^{18} + 26 q^{19} + 164 q^{20} + 220 q^{21} + 152 q^{22} - 69 q^{23} - 308 q^{24} + 95 q^{25} - 115 q^{26} - 10 q^{27} + 314 q^{28} + 266 q^{29} - 466 q^{30} - 90 q^{31} - 592 q^{32} - 588 q^{33} + 826 q^{34} - 704 q^{35} - 621 q^{36} - 128 q^{37} + 888 q^{38} - 6 q^{39} - 170 q^{40} - 30 q^{41} + 560 q^{42} + 90 q^{43} + 694 q^{44} + 180 q^{45} - 92 q^{46} - 1034 q^{47} + 631 q^{48} + 941 q^{49} + 592 q^{50} + 60 q^{51} + 2475 q^{52} - 644 q^{53} + 351 q^{54} - 1176 q^{55} - 2366 q^{56} + 1672 q^{57} - 2325 q^{58} - 1548 q^{59} - 924 q^{60} + 1576 q^{61} + 237 q^{62} - 1076 q^{63} - 357 q^{64} + 1660 q^{65} - 58 q^{66} + 1414 q^{67} + 604 q^{68} - 276 q^{69} - 3916 q^{70} - 66 q^{71} + 1455 q^{72} + 610 q^{73} + 1962 q^{74} + 1846 q^{75} - 3552 q^{76} + 464 q^{77} - 2477 q^{78} - 2160 q^{79} + 2942 q^{80} - 1603 q^{81} - 1139 q^{82} + 106 q^{83} + 2454 q^{84} + 592 q^{85} + 742 q^{86} + 998 q^{87} + 412 q^{88} + 1882 q^{89} + 1760 q^{90} + 748 q^{91} - 552 q^{92} - 1024 q^{93} + 2281 q^{94} - 536 q^{95} + 1599 q^{96} + 98 q^{97} + 3036 q^{98} - 1566 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23
23.4.a.a 23.a 1.a $1$ $1.357$ \(\Q\) None \(-2\) \(-5\) \(-6\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b 23.a 1.a $4$ $1.357$ 4.4.334189.1 None \(2\) \(7\) \(14\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)