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Properties

Label 15.24.a
Level $15$
Weight $24$
Character orbit 15.a
Rep. character $\chi_{15}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 15.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(15))\).

Total New Old
Modular forms 48 16 32
Cusp forms 44 16 28
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)FrickeDim
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(9\)
Minus space\(-\)\(7\)

Trace form

\( 16 q - 3868 q^{2} + 354294 q^{3} + 103317714 q^{4} - 782635446 q^{6} + 8739175864 q^{7} + 39575801724 q^{8} + 502096953744 q^{9} + O(q^{10}) \) \( 16 q - 3868 q^{2} + 354294 q^{3} + 103317714 q^{4} - 782635446 q^{6} + 8739175864 q^{7} + 39575801724 q^{8} + 502096953744 q^{9} + 29394531250 q^{10} - 2173258252720 q^{11} + 4458050224128 q^{12} + 16060600538352 q^{13} - 22559127105156 q^{14} + 17299511718750 q^{15} + 483980954681202 q^{16} - 68613405772912 q^{17} - 121381938567612 q^{18} - 213282009878448 q^{19} + 936171484375000 q^{20} - 1136956277393208 q^{21} - 8820485551064284 q^{22} + 358910481572328 q^{23} + 5143349550903426 q^{24} + 38146972656250000 q^{25} - 80979388166549668 q^{26} + 11118121133111046 q^{27} + 219885226428856972 q^{28} - 27068966593065056 q^{29} + 35429400000000000 q^{30} + 167514325462254208 q^{31} + 110774793049892884 q^{32} + 407128362199090056 q^{33} - 63222933852108772 q^{34} - 633528733203125000 q^{35} + 3242219341699613826 q^{36} + 1576474729293816464 q^{37} - 10629250834205434072 q^{38} + 1633728752991005940 q^{39} + 174987026074218750 q^{40} - 1244917169853120512 q^{41} + 7723596327966830412 q^{42} + 1747250250817913400 q^{43} + 11808851567193624556 q^{44} - 24488694780868061472 q^{46} + 41522444297082029720 q^{47} + 59064411353733287280 q^{48} - 21849268030539174704 q^{49} - 9222030639648437500 q^{50} - 99074300363752660452 q^{51} - 14833810026974468752 q^{52} - 51053735382231077632 q^{53} - 24559929583042300614 q^{54} + 88735531063281250000 q^{55} + 716645236886473399620 q^{56} - 367052147958765064968 q^{57} + 119419834753996315636 q^{58} + 958083963770914123808 q^{59} + 276961670816308593750 q^{60} - 454261644129032186976 q^{61} + 2246133911070131661288 q^{62} + 274244598721718077176 q^{63} + 1159492064439239379418 q^{64} - 1061271758947656250000 q^{65} + 566656652324582926236 q^{66} + 2305683590511659043688 q^{67} - 5034317790484748282504 q^{68} + 1315139949941787084024 q^{69} + 5936237737583789062500 q^{70} - 6485072866324500567248 q^{71} + 1241930592974808965916 q^{72} + 4202917598042231185248 q^{73} - 4437366236178276223676 q^{74} + 844702720642089843750 q^{75} - 1970031747935090307088 q^{76} + 3258739941617606275488 q^{77} - 10804813574166183638592 q^{78} - 12447993220608982624880 q^{79} + 21783089993989843750000 q^{80} + 15756334434937779726096 q^{81} + 43307860686768427873528 q^{82} - 25416486590879743897896 q^{83} - 15390207893748623547924 q^{84} + 8287414312869531250000 q^{85} - 19123821451041745095880 q^{86} + 24444657767044013936004 q^{87} - 170668673858765384523156 q^{88} - 36169674871291794763008 q^{89} + 922431537334863281250 q^{90} - 81525304956399502407472 q^{91} + 288084590256422913561984 q^{92} - 133497360442824408639936 q^{93} - 248412342125377861352680 q^{94} + 96912686745717968750000 q^{95} + 28291559006341885282362 q^{96} + 302164623822234175131968 q^{97} - 93321652511942402438252 q^{98} - 68199146774357506386480 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5
15.24.a.a 15.a 1.a $3$ $50.281$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 15.24.a.a \(-736\) \(-531441\) \(146484375\) \(-4331627008\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-245+\beta _{1})q^{2}-3^{11}q^{3}+(5441980+\cdots)q^{4}+\cdots\)
15.24.a.b 15.a 1.a $4$ $50.281$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 15.24.a.b \(-3246\) \(708588\) \(-195312500\) \(-1053368512\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-812+\beta _{1})q^{2}+3^{11}q^{3}+(4830802+\cdots)q^{4}+\cdots\)
15.24.a.c 15.a 1.a $4$ $50.281$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 15.24.a.c \(1011\) \(-708588\) \(-195312500\) \(11910290672\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(253-\beta _{1})q^{2}-3^{11}q^{3}+(5687506+\cdots)q^{4}+\cdots\)
15.24.a.d 15.a 1.a $5$ $50.281$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 15.24.a.d \(-897\) \(885735\) \(244140625\) \(2213880712\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-179-\beta _{1})q^{2}+3^{11}q^{3}+(8983952+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(15)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)