Properties

Label 23.6.a
Level $23$
Weight $6$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(23))\).

Total New Old
Modular forms 11 9 2
Cusp forms 9 9 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.
\(+\)\(3\)
\(-\)\(6\)

Trace form

\( 9 q - 4 q^{3} + 128 q^{4} - 16 q^{5} + 137 q^{6} + 18 q^{7} + 33 q^{8} + 883 q^{9} + O(q^{10}) \) \( 9 q - 4 q^{3} + 128 q^{4} - 16 q^{5} + 137 q^{6} + 18 q^{7} + 33 q^{8} + 883 q^{9} - 166 q^{10} + 78 q^{11} - 287 q^{12} - 324 q^{13} - 968 q^{14} - 410 q^{15} - 1776 q^{16} - 1296 q^{17} + 1301 q^{18} + 4392 q^{19} - 5620 q^{20} - 6518 q^{21} - 620 q^{22} + 1587 q^{23} - 44 q^{24} + 2619 q^{25} + 6509 q^{26} + 3896 q^{27} - 694 q^{28} + 10400 q^{29} - 6274 q^{30} + 10728 q^{31} + 13256 q^{32} + 11070 q^{33} - 27438 q^{34} - 3224 q^{35} - 13101 q^{36} + 34364 q^{37} + 2700 q^{38} + 10128 q^{39} + 13670 q^{40} - 27060 q^{41} - 3712 q^{42} - 34812 q^{43} - 46034 q^{44} - 35766 q^{45} + 4232 q^{46} - 584 q^{47} - 12089 q^{48} + 40309 q^{49} - 52280 q^{50} - 21294 q^{51} - 10605 q^{52} + 34630 q^{53} + 35583 q^{54} + 47140 q^{55} + 87586 q^{56} - 90320 q^{57} + 85323 q^{58} + 17784 q^{59} + 78084 q^{60} - 44262 q^{61} - 23739 q^{62} - 41588 q^{63} + 39467 q^{64} + 7954 q^{65} - 27754 q^{66} - 25822 q^{67} + 8908 q^{68} + 19044 q^{69} + 257604 q^{70} - 60156 q^{71} - 174009 q^{72} + 30456 q^{73} - 125922 q^{74} - 276344 q^{75} + 189304 q^{76} - 90064 q^{77} + 272251 q^{78} + 95068 q^{79} - 176098 q^{80} + 245081 q^{81} + 211965 q^{82} - 66458 q^{83} - 402954 q^{84} - 86596 q^{85} + 90562 q^{86} + 34592 q^{87} - 277428 q^{88} + 43642 q^{89} - 258940 q^{90} - 98618 q^{91} + 50784 q^{92} + 404918 q^{93} - 134103 q^{94} - 210740 q^{95} - 268041 q^{96} - 14240 q^{97} - 727092 q^{98} + 501192 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(23))\) 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
23.6.a.a 23.a 1.a $3$ $3.689$ 3.3.7925.1 None \(-4\) \(-20\) \(-58\) \(-282\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.6.a.b 23.a 1.a $6$ $3.689$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(4\) \(16\) \(42\) \(300\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{4})q^{3}+(19+\cdots)q^{4}+\cdots\)