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Properties

Label 23.10.a
Level $23$
Weight $10$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $2$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(23))\).

Total New Old
Modular forms 19 17 2
Cusp forms 17 17 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
\(+\)\(7\)
\(-\)\(10\)

Trace form

\( 17 q + 32 q^{2} + 146 q^{3} + 4608 q^{4} - 2276 q^{5} - 1543 q^{6} - 8616 q^{7} + 28401 q^{8} + 84745 q^{9} + O(q^{10}) \) \( 17 q + 32 q^{2} + 146 q^{3} + 4608 q^{4} - 2276 q^{5} - 1543 q^{6} - 8616 q^{7} + 28401 q^{8} + 84745 q^{9} + 1474 q^{10} - 81174 q^{11} + 60577 q^{12} + 11078 q^{13} - 67832 q^{14} + 347320 q^{15} + 1430800 q^{16} - 301206 q^{17} + 2246597 q^{18} - 825798 q^{19} - 3392500 q^{20} + 2109124 q^{21} + 792988 q^{22} + 839523 q^{23} + 1989844 q^{24} + 7754339 q^{25} - 758787 q^{26} + 5020046 q^{27} - 15942102 q^{28} - 3198222 q^{29} + 175166 q^{30} - 1294090 q^{31} + 610344 q^{32} - 20898996 q^{33} + 4616162 q^{34} - 10749904 q^{35} + 8658387 q^{36} - 18252572 q^{37} + 2049956 q^{38} - 26458230 q^{39} - 58981690 q^{40} + 10514474 q^{41} + 112029344 q^{42} - 7369558 q^{43} - 119503186 q^{44} - 72424656 q^{45} + 8954912 q^{46} + 98827686 q^{47} - 142621097 q^{48} + 146632153 q^{49} + 145540120 q^{50} + 63418908 q^{51} + 148826435 q^{52} + 120705064 q^{53} + 35622927 q^{54} + 282856200 q^{55} - 178949470 q^{56} - 25645736 q^{57} - 33356229 q^{58} - 247124084 q^{59} + 208400484 q^{60} - 102318260 q^{61} + 184772901 q^{62} - 178441268 q^{63} + 64026955 q^{64} + 339027084 q^{65} - 1024843498 q^{66} - 58802426 q^{67} - 129158932 q^{68} + 90668484 q^{69} - 554208476 q^{70} - 40561570 q^{71} + 1534141671 q^{72} - 256576838 q^{73} - 1126353786 q^{74} + 609060646 q^{75} - 1537770376 q^{76} + 1171153664 q^{77} + 371613403 q^{78} + 663186704 q^{79} - 2996015778 q^{80} - 97664023 q^{81} - 1564524883 q^{82} + 2618284202 q^{83} + 3474690006 q^{84} + 759665864 q^{85} - 791477334 q^{86} - 1045322842 q^{87} + 1112258828 q^{88} - 1013790702 q^{89} - 4913217940 q^{90} - 2183938212 q^{91} + 429835776 q^{92} - 1793259136 q^{93} - 1407723175 q^{94} + 4158946840 q^{95} - 1847006745 q^{96} + 1242886026 q^{97} + 6221282828 q^{98} - 1409015358 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(23))\) 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
23.10.a.a 23.a 1.a $7$ $11.846$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-89\) \(-2388\) \(-9896\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-13-2\beta _{1}-\beta _{4})q^{3}+(220+\cdots)q^{4}+\cdots\)
23.10.a.b 23.a 1.a $10$ $11.846$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(32\) \(235\) \(112\) \(1280\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(23+\beta _{1}+\beta _{3})q^{3}+(307+\cdots)q^{4}+\cdots\)