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Properties

Label 23.16.a
Level $23$
Weight $16$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $27$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(23))\).

Total New Old
Modular forms 31 27 4
Cusp forms 29 27 2
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
\(+\)\(15\)
\(-\)\(12\)

Trace form

\( 27 q - 256 q^{2} + 5258 q^{3} + 425984 q^{4} - 96452 q^{5} + 482153 q^{6} - 5852552 q^{7} + 2537673 q^{8} + 123817915 q^{9} + O(q^{10}) \) \( 27 q - 256 q^{2} + 5258 q^{3} + 425984 q^{4} - 96452 q^{5} + 482153 q^{6} - 5852552 q^{7} + 2537673 q^{8} + 123817915 q^{9} + 26485442 q^{10} - 34425390 q^{11} + 108375649 q^{12} + 391482314 q^{13} - 500150744 q^{14} - 28448360 q^{15} + 6529113616 q^{16} - 4191331602 q^{17} + 2306131181 q^{18} + 4324568530 q^{19} - 7056803236 q^{20} + 3127471084 q^{21} - 19784160004 q^{22} - 10214476341 q^{23} - 30186988220 q^{24} + 267335081625 q^{25} + 44784122853 q^{26} + 64053813302 q^{27} - 198075350726 q^{28} - 285279726546 q^{29} - 4130792866 q^{30} - 47990796010 q^{31} + 194246339688 q^{32} + 959616400692 q^{33} + 1062051598210 q^{34} - 1062432700144 q^{35} + 1926879213555 q^{36} + 1979275696596 q^{37} - 3660838412572 q^{38} - 2769260840742 q^{39} + 5580961532470 q^{40} - 4622787328546 q^{41} + 7858069584848 q^{42} + 2603276267186 q^{43} + 2674434787454 q^{44} + 5350012859160 q^{45} - 871635314432 q^{46} + 7582963318182 q^{47} - 13285718959361 q^{48} + 14985786359939 q^{49} - 4240467550328 q^{50} + 20692950026988 q^{51} + 7535582059595 q^{52} + 6870054415552 q^{53} - 30981439902825 q^{54} + 6668356884744 q^{55} + 51778293302498 q^{56} + 25053585858088 q^{57} + 26611865797803 q^{58} - 67027665065972 q^{59} + 4749013098516 q^{60} - 7606965364788 q^{61} + 73467018778197 q^{62} - 42776026853684 q^{63} - 69973844826629 q^{64} - 8141429352060 q^{65} + 89623034301206 q^{66} - 43964527137522 q^{67} - 399360836032996 q^{68} - 29785413010356 q^{69} - 265784659117036 q^{70} - 316703642428882 q^{71} - 216415428535353 q^{72} + 44215729377966 q^{73} + 625397162815830 q^{74} + 103808683280926 q^{75} - 129332778066040 q^{76} - 47897159086432 q^{77} - 340456152717701 q^{78} + 282337137813776 q^{79} - 375723228622338 q^{80} + 208538472971411 q^{81} - 152686567605971 q^{82} + 802811762902466 q^{83} - 229224692077818 q^{84} + 194952085567432 q^{85} + 1635198804835290 q^{86} - 1816287056567914 q^{87} - 1464608529418196 q^{88} - 218958229090794 q^{89} + 2140328559580700 q^{90} + 1827577431325484 q^{91} - 334707960741888 q^{92} - 1998697545405568 q^{93} + 2678730950638177 q^{94} + 1639788579527224 q^{95} - 1941312545022417 q^{96} - 2523510450965618 q^{97} - 4807698911553316 q^{98} - 818711263819494 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(23))\) 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
23.16.a.a 23.a 1.a $12$ $32.820$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-256\) \(-1745\) \(-204476\) \(-5717328\) $-$ $\mathrm{SU}(2)$ \(q+(-21+\beta _{1})q^{2}+(-145+\beta _{2})q^{3}+\cdots\)
23.16.a.b 23.a 1.a $15$ $32.820$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(7003\) \(108024\) \(-135224\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(467-\beta _{1}-\beta _{2})q^{3}+(17476+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(23))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(23)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)