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Properties

Label 23.8.a
Level $23$
Weight $8$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(23))\).

Total New Old
Modular forms 15 13 2
Cusp forms 13 13 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
\(+\)\(8\)
\(-\)\(5\)

Trace form

\( 13 q - 16 q^{2} - 28 q^{3} + 896 q^{4} + 388 q^{5} - 1207 q^{6} + 290 q^{7} - 2775 q^{8} + 11683 q^{9} + O(q^{10}) \) \( 13 q - 16 q^{2} - 28 q^{3} + 896 q^{4} + 388 q^{5} - 1207 q^{6} + 290 q^{7} - 2775 q^{8} + 11683 q^{9} + 8242 q^{10} + 6270 q^{11} - 5279 q^{12} + 200 q^{13} + 10696 q^{14} - 37370 q^{15} + 96784 q^{16} + 37068 q^{17} - 83779 q^{18} - 37264 q^{19} + 107804 q^{20} + 25582 q^{21} - 203092 q^{22} - 36501 q^{23} - 259196 q^{24} + 104455 q^{25} - 26331 q^{26} + 31400 q^{27} + 233850 q^{28} - 253212 q^{29} - 155746 q^{30} + 124232 q^{31} - 1016856 q^{32} + 127554 q^{33} - 492414 q^{34} + 157016 q^{35} + 2379507 q^{36} - 466200 q^{37} - 306124 q^{38} + 824832 q^{39} + 1022710 q^{40} + 131504 q^{41} - 2136688 q^{42} + 1119932 q^{43} + 1599806 q^{44} + 1697490 q^{45} - 194672 q^{46} - 332904 q^{47} - 505313 q^{48} - 2060623 q^{49} + 3029752 q^{50} + 2563962 q^{51} - 3435925 q^{52} + 1100758 q^{53} - 8052873 q^{54} + 178724 q^{55} - 2716702 q^{56} + 7045840 q^{57} + 645099 q^{58} + 272080 q^{59} - 19632684 q^{60} - 2696542 q^{61} - 2277483 q^{62} + 2546764 q^{63} + 7875515 q^{64} - 2922090 q^{65} + 15485078 q^{66} + 1712466 q^{67} + 7416284 q^{68} - 1314036 q^{69} + 8077524 q^{70} - 1906780 q^{71} - 14681145 q^{72} + 2147348 q^{73} + 1765446 q^{74} - 11646944 q^{75} + 4009288 q^{76} - 8786560 q^{77} - 16787141 q^{78} - 235076 q^{79} + 20983422 q^{80} + 2298893 q^{81} + 24898605 q^{82} - 4118794 q^{83} + 10292934 q^{84} + 1228492 q^{85} - 17707254 q^{86} + 22013600 q^{87} - 21225300 q^{88} + 10585266 q^{89} + 44050700 q^{90} + 5729214 q^{91} - 4672128 q^{92} - 16182766 q^{93} - 1579647 q^{94} - 28722596 q^{95} - 4620465 q^{96} + 12189100 q^{97} + 22688396 q^{98} - 34528176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(23))\) 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
23.8.a.a 23.a 1.a $5$ $7.185$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-16\) \(-68\) \(-56\) \(-1156\) $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
23.8.a.b 23.a 1.a $8$ $7.185$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(40\) \(444\) \(1446\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\)