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Properties

Label 30.24.a
Level $30$
Weight $24$
Character orbit 30.a
Rep. character $\chi_{30}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $8$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 30.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(30))\).

Total New Old
Modular forms 142 14 128
Cusp forms 134 14 120
Eisenstein series 8 0 8

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

\(2\)\(3\)\(5\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(8\)
Minus space\(-\)\(6\)

Trace form

\( 14 q - 354294 q^{3} + 58720256 q^{4} + 6194382628 q^{7} + 439334834526 q^{9} + O(q^{10}) \) \( 14 q - 354294 q^{3} + 58720256 q^{4} + 6194382628 q^{7} + 439334834526 q^{9} - 200000000000 q^{10} + 1310826277884 q^{11} - 1486016741376 q^{12} - 2932605847472 q^{13} - 51178626392064 q^{14} + 246290604621824 q^{16} + 327633084607848 q^{17} + 477351372259888 q^{19} - 1951280156430612 q^{21} + 3549299690102784 q^{22} - 20989878622693608 q^{23} + 33378601074218750 q^{25} + 39027570863775744 q^{26} - 11118121133111046 q^{27} + 25981123834150912 q^{28} + 27314559277926792 q^{29} - 35429400000000000 q^{30} + 25711041032411080 q^{31} - 612088298343272844 q^{33} + 446730438861889536 q^{34} + 982834041210937500 q^{35} + 1842703853791739904 q^{36} - 902269585114402280 q^{37} + 6925959296901169152 q^{38} - 3358537082266238352 q^{39} - 838860800000000000 q^{40} - 5056044442180543908 q^{41} - 3346588049779777536 q^{42} + 1529066243519179720 q^{43} + 5498003900633972736 q^{44} - 18811376517552095232 q^{46} - 518354146421116944 q^{47} - 6232805962420322304 q^{48} + 64607840908219949358 q^{49} + 100586413368704217528 q^{51} - 12300240436475199488 q^{52} - 156474608507892052656 q^{53} + 25921977274804687500 q^{55} - 214658717390739603456 q^{56} + 187213848946390557072 q^{57} + 199810208890413539328 q^{58} - 239304956807325715860 q^{59} - 134256058924878878756 q^{61} - 772724785947029225472 q^{62} + 194386290490222072452 q^{63} + 1033017668127734890496 q^{64} + 6038954767382812500 q^{65} + 73402703861799297024 q^{66} - 981792685183902999872 q^{67} + 1374192757303035297792 q^{68} - 2497117769490107589048 q^{69} - 790930697200000000000 q^{70} + 5371899580364456694024 q^{71} - 5816832008632865134412 q^{73} + 5691360270071151157248 q^{74} - 844702720642089843750 q^{75} + 2002156770075137277952 q^{76} - 14700699748245577647648 q^{77} - 1892446074469305851904 q^{78} + 20818459836522876186424 q^{79} + 13786792630570557260334 q^{81} - 22584284773549261553664 q^{82} + 24774972205592287012128 q^{83} - 8184262165237541634048 q^{84} + 16105808678840039062500 q^{85} - 11983823880999902674944 q^{86} + 8769487489990639325208 q^{87} + 14886841887396867342336 q^{88} + 29166591819045653906004 q^{89} - 6276211921800000000000 q^{90} + 29506024533983623846088 q^{91} - 88037931866678290808832 q^{92} + 116209302058290559624920 q^{93} + 194003326190545647796224 q^{94} - 141644062862178515625000 q^{95} - 218892728625652093528580 q^{97} + 89661504953761981169664 q^{98} + 41135117563321402387356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(30))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
30.24.a.a 30.a 1.a $1$ $100.561$ \(\Q\) None 30.24.a.a \(-2048\) \(177147\) \(-48828125\) \(3069411548\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}-5^{11}q^{5}+\cdots\)
30.24.a.b 30.a 1.a $1$ $100.561$ \(\Q\) None 30.24.a.b \(2048\) \(177147\) \(48828125\) \(-8229227776\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}+5^{11}q^{5}+\cdots\)
30.24.a.c 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.c \(-4096\) \(-354294\) \(-97656250\) \(-2282862008\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}-5^{11}q^{5}+\cdots\)
30.24.a.d 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.d \(-4096\) \(-354294\) \(97656250\) \(10526504992\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}+5^{11}q^{5}+\cdots\)
30.24.a.e 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.e \(-4096\) \(354294\) \(97656250\) \(4278918616\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}+5^{11}q^{5}+\cdots\)
30.24.a.f 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.f \(4096\) \(-354294\) \(-97656250\) \(-6224150936\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}-5^{11}q^{5}+\cdots\)
30.24.a.g 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.g \(4096\) \(-354294\) \(97656250\) \(6585216064\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}+5^{11}q^{5}+\cdots\)
30.24.a.h 30.a 1.a $2$ $100.561$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 30.24.a.h \(4096\) \(354294\) \(-97656250\) \(-1529427872\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}-5^{11}q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(30))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(30)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)