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Properties

Label 5.12.a
Level $5$
Weight $12$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $6$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(5))\).

Total New Old
Modular forms 7 3 4
Cusp forms 5 3 2
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.

\(5\)Dim
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3 q + 14 q^{2} - 1012 q^{3} + 6084 q^{4} - 3125 q^{5} + 33256 q^{6} + 40344 q^{7} - 346200 q^{8} + 429271 q^{9} + O(q^{10}) \) \( 3 q + 14 q^{2} - 1012 q^{3} + 6084 q^{4} - 3125 q^{5} + 33256 q^{6} + 40344 q^{7} - 346200 q^{8} + 429271 q^{9} + 168750 q^{10} - 1086964 q^{11} - 1220576 q^{12} + 3040218 q^{13} + 737568 q^{14} - 1787500 q^{15} + 4433808 q^{16} - 2406346 q^{17} + 2755958 q^{18} + 4945860 q^{19} - 24587500 q^{20} + 17740536 q^{21} - 105430632 q^{22} + 26485848 q^{23} + 201348480 q^{24} + 29296875 q^{25} - 93479164 q^{26} - 242961400 q^{27} + 179345712 q^{28} + 163837090 q^{29} - 272225000 q^{30} + 415992096 q^{31} - 476025056 q^{32} - 70979744 q^{33} + 318732348 q^{34} - 235800000 q^{35} - 219085612 q^{36} - 270337326 q^{37} + 928850600 q^{38} - 327962728 q^{39} + 457125000 q^{40} - 554400074 q^{41} + 1902541008 q^{42} - 1129907292 q^{43} + 175433008 q^{44} + 1471759375 q^{45} - 1571769984 q^{46} + 221408384 q^{47} - 5130637952 q^{48} - 3610791021 q^{49} + 136718750 q^{50} + 5250194296 q^{51} + 13174967064 q^{52} + 493431938 q^{53} - 16555690640 q^{54} + 466837500 q^{55} - 2235656160 q^{56} + 5021442800 q^{57} + 9757106100 q^{58} + 8243084780 q^{59} + 8229700000 q^{60} - 12415015014 q^{61} - 22735073952 q^{62} - 10750886232 q^{63} + 9182013504 q^{64} - 11838443750 q^{65} + 9648059072 q^{66} + 19529964204 q^{67} - 1251711608 q^{68} + 19869613032 q^{69} - 6035550000 q^{70} + 9971527816 q^{71} - 63347763000 q^{72} - 20102028402 q^{73} + 58862619508 q^{74} - 9882812500 q^{75} - 986914320 q^{76} - 26504706672 q^{77} + 120428573776 q^{78} - 24071709360 q^{79} - 23679550000 q^{80} + 47602946083 q^{81} - 68124845412 q^{82} + 16503964428 q^{83} - 28385169792 q^{84} - 15756956250 q^{85} - 116541245224 q^{86} - 21134853400 q^{87} - 33934826400 q^{88} + 50501550270 q^{89} + 87037493750 q^{90} + 97204540416 q^{91} + 232124189904 q^{92} - 301987859184 q^{93} - 5091788112 q^{94} - 17827437500 q^{95} - 14295226624 q^{96} + 123413770134 q^{97} + 73456940302 q^{98} - 92309175748 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.12.a.a 5.a 1.a $1$ $3.842$ \(\Q\) None \(34\) \(-792\) \(3125\) \(-17556\) $-$ $\mathrm{SU}(2)$ \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b 5.a 1.a $2$ $3.842$ \(\Q(\sqrt{151}) \) None \(-20\) \(-220\) \(-6250\) \(57900\) $+$ $\mathrm{SU}(2)$ \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)