Properties

Label 23.7
Level 23
Weight 7
Dimension 121
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 308
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(308\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(23))\).

Total New Old
Modular forms 143 143 0
Cusp forms 121 121 0
Eisenstein series 22 22 0

Trace form

\( 121q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} + O(q^{10}) \) \( 121q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} - 11q^{10} - 11q^{11} - 11q^{12} - 11q^{13} - 11q^{14} + 10461q^{15} - 31691q^{16} - 11451q^{17} + 13365q^{18} + 15829q^{19} + 78837q^{20} + 40909q^{21} - 32923q^{23} - 179542q^{24} - 69707q^{25} - 54571q^{26} - 18491q^{27} + 101365q^{28} + 58509q^{29} + 311157q^{30} + 59389q^{31} - 59851q^{32} - 234267q^{33} + 400015q^{34} - 71511q^{35} - 601436q^{36} - 446699q^{37} - 275286q^{38} + 64141q^{39} + 626989q^{40} + 235389q^{41} + 1274119q^{42} + 428989q^{43} + 434434q^{44} - 542531q^{46} - 518430q^{47} - 1390675q^{48} - 1141283q^{49} - 1203136q^{50} - 463331q^{51} - 247181q^{52} + 183909q^{53} + 3219117q^{54} + 1417405q^{55} + 175560q^{56} + 78661q^{57} - 970706q^{58} - 1638087q^{59} - 2858581q^{60} + 495253q^{61} + 1544389q^{62} + 1713789q^{63} + 2973685q^{64} + 2406085q^{65} + 2124936q^{66} + 290389q^{67} - 770451q^{69} - 2392918q^{70} - 2086931q^{71} - 5921630q^{72} - 1024331q^{73} - 1038180q^{74} + 1483669q^{75} - 1754258q^{76} - 2268651q^{77} - 6512781q^{78} - 833723q^{79} + 2796838q^{80} + 138413q^{81} + 3609199q^{82} + 2924229q^{83} + 6932651q^{84} + 4488385q^{85} + 1596771q^{86} + 9184549q^{87} + 5363325q^{88} + 2950849q^{89} + 5004362q^{90} - 2477486q^{92} - 6461422q^{93} - 6892600q^{94} - 3255219q^{95} - 13057616q^{96} - 6375215q^{97} - 11621907q^{98} - 16096091q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.7.b \(\chi_{23}(22, \cdot)\) 23.7.b.a 1 1
23.7.b.b 2
23.7.b.c 8
23.7.d \(\chi_{23}(5, \cdot)\) 23.7.d.a 110 10

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 7 T + 64 T^{2} \))(\( 1 - 7 T - 15 T^{2} - 448 T^{3} + 4096 T^{4} \))(\( ( 1 - 4 T + 94 T^{2} + 152 T^{3} + 4672 T^{4} + 9728 T^{5} + 385024 T^{6} - 1048576 T^{7} + 16777216 T^{8} )^{2} \))
$3$ (\( 1 + 38 T + 729 T^{2} \))(\( 1 - 38 T + 715 T^{2} - 27702 T^{3} + 531441 T^{4} \))(\( ( 1 - 15 T + 1959 T^{2} - 19512 T^{3} + 1780470 T^{4} - 14224248 T^{5} + 1041092919 T^{6} - 5811307335 T^{7} + 282429536481 T^{8} )^{2} \))
$5$ (\( ( 1 - 125 T )( 1 + 125 T ) \))(\( ( 1 - 125 T )^{2}( 1 + 125 T )^{2} \))(\( 1 - 29900 T^{2} + 1104806800 T^{4} - 20380789554500 T^{6} + 420567476701618750 T^{8} - \)\(49\!\cdots\!00\)\( T^{10} + \)\(65\!\cdots\!00\)\( T^{12} - \)\(43\!\cdots\!00\)\( T^{14} + \)\(35\!\cdots\!25\)\( T^{16} \))
$7$ (\( ( 1 - 343 T )( 1 + 343 T ) \))(\( ( 1 - 343 T )^{2}( 1 + 343 T )^{2} \))(\( 1 - 280700 T^{2} + 73550518480 T^{4} - 11717143708525364 T^{6} + \)\(16\!\cdots\!10\)\( T^{8} - \)\(16\!\cdots\!64\)\( T^{10} + \)\(14\!\cdots\!80\)\( T^{12} - \)\(74\!\cdots\!00\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} \))
$11$ (\( ( 1 - 1331 T )( 1 + 1331 T ) \))(\( ( 1 - 1331 T )^{2}( 1 + 1331 T )^{2} \))(\( 1 - 2477780 T^{2} + 7228525026880 T^{4} - 15113704212521563196 T^{6} + \)\(33\!\cdots\!30\)\( T^{8} - \)\(47\!\cdots\!16\)\( T^{10} + \)\(71\!\cdots\!80\)\( T^{12} - \)\(76\!\cdots\!80\)\( T^{14} + \)\(97\!\cdots\!81\)\( T^{16} \))
$13$ (\( 1 - 1082 T + 4826809 T^{2} \))(\( 1 + 1082 T - 3656085 T^{2} + 5222607338 T^{3} + 23298085122481 T^{4} \))(\( ( 1 + 553 T + 17128489 T^{2} + 7444938358 T^{3} + 119770998891094 T^{4} + 35935295470839622 T^{5} + \)\(39\!\cdots\!09\)\( T^{6} + \)\(62\!\cdots\!37\)\( T^{7} + \)\(54\!\cdots\!61\)\( T^{8} )^{2} \))
$17$ (\( ( 1 - 4913 T )( 1 + 4913 T ) \))(\( ( 1 - 4913 T )^{2}( 1 + 4913 T )^{2} \))(\( 1 - 118558484 T^{2} + 7306395063255136 T^{4} - \)\(29\!\cdots\!64\)\( T^{6} + \)\(83\!\cdots\!10\)\( T^{8} - \)\(17\!\cdots\!04\)\( T^{10} + \)\(24\!\cdots\!56\)\( T^{12} - \)\(23\!\cdots\!04\)\( T^{14} + \)\(11\!\cdots\!41\)\( T^{16} \))
$19$ (\( ( 1 - 6859 T )( 1 + 6859 T ) \))(\( ( 1 - 6859 T )^{2}( 1 + 6859 T )^{2} \))(\( 1 - 53526176 T^{2} + 5850719973451756 T^{4} - \)\(33\!\cdots\!76\)\( T^{6} + \)\(16\!\cdots\!70\)\( T^{8} - \)\(75\!\cdots\!36\)\( T^{10} + \)\(28\!\cdots\!76\)\( T^{12} - \)\(58\!\cdots\!56\)\( T^{14} + \)\(23\!\cdots\!41\)\( T^{16} \))
$23$ (\( 1 + 12167 T \))(\( ( 1 + 12167 T )^{2} \))(\( 1 - 18304 T + 173040868 T^{2} + 3121728858272 T^{3} - 56035372946889290 T^{4} + \)\(46\!\cdots\!08\)\( T^{5} + \)\(37\!\cdots\!28\)\( T^{6} - \)\(59\!\cdots\!76\)\( T^{7} + \)\(48\!\cdots\!41\)\( T^{8} \))
$29$ (\( 1 - 30746 T + 594823321 T^{2} \))(\( 1 + 30746 T + 350493195 T^{2} + 18288437827466 T^{3} + 353814783205469041 T^{4} \))(\( ( 1 + 43061 T + 1464237061 T^{2} + 47992044406874 T^{3} + 1397948244432450334 T^{4} + \)\(28\!\cdots\!54\)\( T^{5} + \)\(51\!\cdots\!01\)\( T^{6} + \)\(90\!\cdots\!21\)\( T^{7} + \)\(12\!\cdots\!81\)\( T^{8} )^{2} \))
$31$ (\( 1 - 58754 T + 887503681 T^{2} \))(\( 1 + 58754 T + 2564528835 T^{2} + 52144391273474 T^{3} + 787662783788549761 T^{4} \))(\( ( 1 + 14245 T + 2476524571 T^{2} + 10920090216316 T^{3} + 2664056385438398830 T^{4} + \)\(96\!\cdots\!96\)\( T^{5} + \)\(19\!\cdots\!31\)\( T^{6} + \)\(99\!\cdots\!45\)\( T^{7} + \)\(62\!\cdots\!21\)\( T^{8} )^{2} \))
$37$ (\( ( 1 - 50653 T )( 1 + 50653 T ) \))(\( ( 1 - 50653 T )^{2}( 1 + 50653 T )^{2} \))(\( 1 - 9816325964 T^{2} + 52876271569275514576 T^{4} - \)\(20\!\cdots\!44\)\( T^{6} + \)\(59\!\cdots\!70\)\( T^{8} - \)\(13\!\cdots\!64\)\( T^{10} + \)\(22\!\cdots\!36\)\( T^{12} - \)\(28\!\cdots\!24\)\( T^{14} + \)\(18\!\cdots\!21\)\( T^{16} \))
$41$ (\( 1 - 43634 T + 4750104241 T^{2} \))(\( 1 + 43634 T - 2846178285 T^{2} + 207266048451794 T^{3} + 22563490300366186081 T^{4} \))(\( ( 1 - 107227 T + 16198264261 T^{2} - 983547824340094 T^{3} + 95896046334792313198 T^{4} - \)\(46\!\cdots\!54\)\( T^{5} + \)\(36\!\cdots\!41\)\( T^{6} - \)\(11\!\cdots\!67\)\( T^{7} + \)\(50\!\cdots\!61\)\( T^{8} )^{2} \))
$43$ (\( ( 1 - 79507 T )( 1 + 79507 T ) \))(\( ( 1 - 79507 T )^{2}( 1 + 79507 T )^{2} \))(\( 1 - 25744087184 T^{2} + \)\(33\!\cdots\!96\)\( T^{4} - \)\(29\!\cdots\!44\)\( T^{6} + \)\(20\!\cdots\!50\)\( T^{8} - \)\(11\!\cdots\!44\)\( T^{10} + \)\(52\!\cdots\!96\)\( T^{12} - \)\(16\!\cdots\!84\)\( T^{14} + \)\(25\!\cdots\!01\)\( T^{16} \))
$47$ (\( 1 + 205342 T + 10779215329 T^{2} \))(\( 1 - 205342 T + 31386121635 T^{2} - 2213425634087518 T^{3} + \)\(11\!\cdots\!41\)\( T^{4} \))(\( ( 1 + 64109 T + 33021667459 T^{2} + 1897937629715612 T^{3} + \)\(47\!\cdots\!78\)\( T^{4} + \)\(20\!\cdots\!48\)\( T^{5} + \)\(38\!\cdots\!19\)\( T^{6} + \)\(80\!\cdots\!01\)\( T^{7} + \)\(13\!\cdots\!81\)\( T^{8} )^{2} \))
$53$ (\( ( 1 - 148877 T )( 1 + 148877 T ) \))(\( ( 1 - 148877 T )^{2}( 1 + 148877 T )^{2} \))(\( 1 - 8981860112 T^{2} - \)\(19\!\cdots\!32\)\( T^{4} - \)\(12\!\cdots\!84\)\( T^{6} + \)\(27\!\cdots\!70\)\( T^{8} - \)\(60\!\cdots\!44\)\( T^{10} - \)\(47\!\cdots\!92\)\( T^{12} - \)\(10\!\cdots\!52\)\( T^{14} + \)\(58\!\cdots\!61\)\( T^{16} \))
$59$ (\( 1 + 253942 T + 42180533641 T^{2} \))(\( ( 1 + 253942 T + 42180533641 T^{2} )^{2} \))(\( ( 1 - 147928 T + 72060379732 T^{2} - 6580944491921800 T^{3} + \)\(28\!\cdots\!02\)\( T^{4} - \)\(27\!\cdots\!00\)\( T^{5} + \)\(12\!\cdots\!92\)\( T^{6} - \)\(11\!\cdots\!88\)\( T^{7} + \)\(31\!\cdots\!61\)\( T^{8} )^{2} \))
$61$ (\( ( 1 - 226981 T )( 1 + 226981 T ) \))(\( ( 1 - 226981 T )^{2}( 1 + 226981 T )^{2} \))(\( 1 - 276140835776 T^{2} + \)\(38\!\cdots\!36\)\( T^{4} - \)\(33\!\cdots\!16\)\( T^{6} + \)\(20\!\cdots\!70\)\( T^{8} - \)\(88\!\cdots\!36\)\( T^{10} + \)\(26\!\cdots\!76\)\( T^{12} - \)\(51\!\cdots\!36\)\( T^{14} + \)\(49\!\cdots\!81\)\( T^{16} \))
$67$ (\( ( 1 - 300763 T )( 1 + 300763 T ) \))(\( ( 1 - 300763 T )^{2}( 1 + 300763 T )^{2} \))(\( 1 - 557668104404 T^{2} + \)\(14\!\cdots\!96\)\( T^{4} - \)\(23\!\cdots\!44\)\( T^{6} + \)\(26\!\cdots\!90\)\( T^{8} - \)\(19\!\cdots\!84\)\( T^{10} + \)\(98\!\cdots\!16\)\( T^{12} - \)\(30\!\cdots\!24\)\( T^{14} + \)\(44\!\cdots\!41\)\( T^{16} \))
$71$ (\( 1 - 667154 T + 128100283921 T^{2} \))(\( 1 + 667154 T + 316994175795 T^{2} + 85462616819030834 T^{3} + \)\(16\!\cdots\!41\)\( T^{4} \))(\( ( 1 + 173393 T + 329115845071 T^{2} + 63816603380254736 T^{3} + \)\(52\!\cdots\!78\)\( T^{4} + \)\(81\!\cdots\!56\)\( T^{5} + \)\(54\!\cdots\!11\)\( T^{6} + \)\(36\!\cdots\!73\)\( T^{7} + \)\(26\!\cdots\!81\)\( T^{8} )^{2} \))
$73$ (\( 1 - 725042 T + 151334226289 T^{2} \))(\( 1 + 725042 T + 374351675475 T^{2} + 109723670097029138 T^{3} + \)\(22\!\cdots\!21\)\( T^{4} \))(\( ( 1 + 256393 T + 391062106009 T^{2} + 93954929931882478 T^{3} + \)\(82\!\cdots\!74\)\( T^{4} + \)\(14\!\cdots\!42\)\( T^{5} + \)\(89\!\cdots\!89\)\( T^{6} + \)\(88\!\cdots\!17\)\( T^{7} + \)\(52\!\cdots\!41\)\( T^{8} )^{2} \))
$79$ (\( ( 1 - 493039 T )( 1 + 493039 T ) \))(\( ( 1 - 493039 T )^{2}( 1 + 493039 T )^{2} \))(\( 1 - 1143298424936 T^{2} + \)\(71\!\cdots\!76\)\( T^{4} - \)\(29\!\cdots\!76\)\( T^{6} + \)\(84\!\cdots\!90\)\( T^{8} - \)\(17\!\cdots\!16\)\( T^{10} + \)\(25\!\cdots\!56\)\( T^{12} - \)\(23\!\cdots\!56\)\( T^{14} + \)\(12\!\cdots\!61\)\( T^{16} \))
$83$ (\( ( 1 - 571787 T )( 1 + 571787 T ) \))(\( ( 1 - 571787 T )^{2}( 1 + 571787 T )^{2} \))(\( 1 - 736069692020 T^{2} + \)\(31\!\cdots\!20\)\( T^{4} - \)\(14\!\cdots\!84\)\( T^{6} + \)\(58\!\cdots\!70\)\( T^{8} - \)\(15\!\cdots\!24\)\( T^{10} + \)\(35\!\cdots\!20\)\( T^{12} - \)\(89\!\cdots\!20\)\( T^{14} + \)\(13\!\cdots\!41\)\( T^{16} \))
$89$ (\( ( 1 - 704969 T )( 1 + 704969 T ) \))(\( ( 1 - 704969 T )^{2}( 1 + 704969 T )^{2} \))(\( 1 - 2242956565880 T^{2} + \)\(27\!\cdots\!20\)\( T^{4} - \)\(21\!\cdots\!56\)\( T^{6} + \)\(12\!\cdots\!70\)\( T^{8} - \)\(53\!\cdots\!76\)\( T^{10} + \)\(16\!\cdots\!20\)\( T^{12} - \)\(33\!\cdots\!80\)\( T^{14} + \)\(37\!\cdots\!81\)\( T^{16} \))
$97$ (\( ( 1 - 912673 T )( 1 + 912673 T ) \))(\( ( 1 - 912673 T )^{2}( 1 + 912673 T )^{2} \))(\( 1 - 3628890295124 T^{2} + \)\(75\!\cdots\!36\)\( T^{4} - \)\(10\!\cdots\!44\)\( T^{6} + \)\(10\!\cdots\!10\)\( T^{8} - \)\(70\!\cdots\!04\)\( T^{10} + \)\(36\!\cdots\!16\)\( T^{12} - \)\(12\!\cdots\!04\)\( T^{14} + \)\(23\!\cdots\!61\)\( T^{16} \))
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