Properties

Label 23.4.a
Level 23
Weight 4
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.4.a.a \(1\) \(1.357\) \(\Q\) None \(-2\) \(-5\) \(-6\) \(-8\) \(-\) \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b \(4\) \(1.357\) 4.4.334189.1 None \(2\) \(7\) \(14\) \(16\) \(+\) \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 8 T^{2} \))(\( 1 - 2 T + 8 T^{2} + 13 T^{3} + 2 T^{4} + 104 T^{5} + 512 T^{6} - 1024 T^{7} + 4096 T^{8} \))
$3$ (\( 1 + 5 T + 27 T^{2} \))(\( 1 - 7 T + 95 T^{2} - 436 T^{3} + 3520 T^{4} - 11772 T^{5} + 69255 T^{6} - 137781 T^{7} + 531441 T^{8} \))
$5$ (\( 1 + 6 T + 125 T^{2} \))(\( 1 - 14 T + 256 T^{2} - 418 T^{3} + 12846 T^{4} - 52250 T^{5} + 4000000 T^{6} - 27343750 T^{7} + 244140625 T^{8} \))
$7$ (\( 1 + 8 T + 343 T^{2} \))(\( 1 - 16 T + 204 T^{2} - 5384 T^{3} + 206630 T^{4} - 1846712 T^{5} + 24000396 T^{6} - 645657712 T^{7} + 13841287201 T^{8} \))
$11$ (\( 1 - 34 T + 1331 T^{2} \))(\( 1 - 8 T + 2836 T^{2} + 24208 T^{3} + 3924870 T^{4} + 32220848 T^{5} + 5024146996 T^{6} - 18863581528 T^{7} + 3138428376721 T^{8} \))
$13$ (\( 1 + 57 T + 2197 T^{2} \))(\( 1 - 111 T + 9317 T^{2} - 606318 T^{3} + 32607938 T^{4} - 1332080646 T^{5} + 44971379453 T^{6} - 1177099430403 T^{7} + 23298085122481 T^{8} \))
$17$ (\( 1 + 80 T + 4913 T^{2} \))(\( 1 - 98 T + 18644 T^{2} - 1340174 T^{3} + 134065526 T^{4} - 6584274862 T^{5} + 450020836436 T^{6} - 11621611896706 T^{7} + 582622237229761 T^{8} \))
$19$ (\( 1 + 70 T + 6859 T^{2} \))(\( 1 - 96 T + 6228 T^{2} - 664352 T^{3} + 58340886 T^{4} - 4556790368 T^{5} + 293001746868 T^{6} - 30978018986784 T^{7} + 2213314919066161 T^{8} \))
$23$ (\( 1 - 23 T \))(\( ( 1 + 23 T )^{4} \))
$29$ (\( 1 - 245 T + 24389 T^{2} \))(\( 1 - 21 T + 43029 T^{2} + 1233294 T^{3} + 1234620970 T^{4} + 30078807366 T^{5} + 25594652679309 T^{6} - 304650065493249 T^{7} + 353814783205469041 T^{8} \))
$31$ (\( 1 - 103 T + 29791 T^{2} \))(\( 1 + 193 T + 118479 T^{2} + 15737568 T^{3} + 5226103696 T^{4} + 468837888288 T^{5} + 105150548621199 T^{6} + 5102847077009503 T^{7} + 787662783788549761 T^{8} \))
$37$ (\( 1 + 298 T + 50653 T^{2} \))(\( 1 - 170 T + 67600 T^{2} - 14886854 T^{3} + 4106178254 T^{4} - 754063815662 T^{5} + 173443105248400 T^{6} - 22093495765163090 T^{7} + 6582952005840035281 T^{8} \))
$41$ (\( 1 - 95 T + 68921 T^{2} \))(\( 1 + 125 T + 262021 T^{2} + 25302094 T^{3} + 26646757314 T^{4} + 1743845620574 T^{5} + 1244627063331061 T^{6} + 40922741799245125 T^{7} + 22563490300366186081 T^{8} \))
$43$ (\( 1 - 88 T + 79507 T^{2} \))(\( 1 - 2 T + 237596 T^{2} - 6518130 T^{3} + 25216368470 T^{4} - 518236961910 T^{5} + 1501930574990204 T^{6} - 1005185223873686 T^{7} + 39959630797262576401 T^{8} \))
$47$ (\( 1 + 357 T + 103823 T^{2} \))(\( 1 + 677 T + 441943 T^{2} + 176800520 T^{3} + 67040162064 T^{4} + 18355960387960 T^{5} + 4763798760144247 T^{6} + 757651330290573259 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))
$53$ (\( 1 + 414 T + 148877 T^{2} \))(\( 1 + 230 T + 261896 T^{2} + 22166738 T^{3} + 41283664862 T^{4} + 3300117453226 T^{5} + 5804757522240584 T^{6} + 758945626114490590 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))
$59$ (\( 1 + 408 T + 205379 T^{2} \))(\( 1 + 1140 T + 1222796 T^{2} + 746561364 T^{3} + 419058243382 T^{4} + 153328026376956 T^{5} + 51578187814080236 T^{6} + 9875815233266630460 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))
$61$ (\( 1 - 822 T + 226981 T^{2} \))(\( 1 - 754 T + 1043632 T^{2} - 513944326 T^{3} + 370106759150 T^{4} - 116655597059806 T^{5} + 53768311335119152 T^{6} - 8817386153996942314 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))
$67$ (\( 1 - 926 T + 300763 T^{2} \))(\( 1 - 488 T + 942484 T^{2} - 309364928 T^{3} + 384185528102 T^{4} - 93045523840064 T^{5} + 85255577860167796 T^{6} - 13276788785391934136 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))
$71$ (\( 1 - 335 T + 357911 T^{2} \))(\( 1 + 401 T + 743943 T^{2} + 132494832 T^{3} + 270748693008 T^{4} + 47421357815952 T^{5} + 95299309521040503 T^{6} + 18385248788098061431 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} \))
$73$ (\( 1 + 899 T + 389017 T^{2} \))(\( 1 - 1509 T + 1981945 T^{2} - 1668507366 T^{3} + 1224656390878 T^{4} - 649077729999222 T^{5} + 299936113122352105 T^{6} - 88837224342776280717 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))
$79$ (\( 1 + 1322 T + 493039 T^{2} \))(\( 1 + 838 T + 1791072 T^{2} + 941948694 T^{3} + 1218053106718 T^{4} + 464417442141066 T^{5} + 435387135134908512 T^{6} + \)\(10\!\cdots\!22\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))
$83$ (\( 1 + 36 T + 571787 T^{2} \))(\( 1 - 142 T + 1903548 T^{2} - 155539494 T^{3} + 1529982465222 T^{4} - 88935460655778 T^{5} + 622346693845813212 T^{6} - 26545516247990737226 T^{7} + \)\(10\!\cdots\!61\)\( T^{8} \))
$89$ (\( 1 + 460 T + 704969 T^{2} \))(\( 1 - 2342 T + 4281932 T^{2} - 4865072738 T^{3} + 4830100875446 T^{4} - 3429725463035122 T^{5} + 2128040093167216652 T^{6} - \)\(82\!\cdots\!78\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))
$97$ (\( 1 + 964 T + 912673 T^{2} \))(\( 1 - 1062 T + 1869900 T^{2} - 2186621722 T^{3} + 1807325015910 T^{4} - 1995670606882906 T^{5} + 1557574352016737100 T^{6} - \)\(80\!\cdots\!54\)\( T^{7} + \)\(69\!\cdots\!41\)\( T^{8} \))
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