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Properties

Label 5.28.a
Level $5$
Weight $28$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_0(5))\).

Total New Old
Modular forms 15 9 6
Cusp forms 13 9 4
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
\(+\)\(5\)
\(-\)\(4\)

Trace form

\( 9 q + 8366 q^{2} + 2396882 q^{3} + 610122052 q^{4} - 1220703125 q^{5} - 121566186392 q^{6} - 59368836794 q^{7} + 5027709753000 q^{8} + 35048193812833 q^{9} + O(q^{10}) \) \( 9 q + 8366 q^{2} + 2396882 q^{3} + 610122052 q^{4} - 1220703125 q^{5} - 121566186392 q^{6} - 59368836794 q^{7} + 5027709753000 q^{8} + 35048193812833 q^{9} - 38410644531250 q^{10} - 141735148701952 q^{11} + 2377886391976096 q^{12} - 1012815632042278 q^{13} - 2552535776499936 q^{14} - 8965432128906250 q^{15} + 113059186465580944 q^{16} + 38917800437135786 q^{17} - 31339141140990058 q^{18} - 783503002261327900 q^{19} + 130788051757812500 q^{20} - 2264183420722160772 q^{21} + 4676112451451955352 q^{22} - 632995519432981038 q^{23} - 554143941021052800 q^{24} + 13411045074462890625 q^{25} + 48291921754192905668 q^{26} + 68185053143826911900 q^{27} - 147352560821374590032 q^{28} + 70888311306879749950 q^{29} - 244550965712890625000 q^{30} + 330485814145490247508 q^{31} - 47879097675000530144 q^{32} - 5142254806277878496 q^{33} + 90621312994194620284 q^{34} - 452467691901855468750 q^{35} + 4090796984872858269524 q^{36} - 817006559264550523254 q^{37} - 9902938987282973805400 q^{38} + 5108542235033258291636 q^{39} - 5689875041748046875000 q^{40} - 766438468438598090762 q^{41} + 33021053090030958664272 q^{42} - 19694395094510480180758 q^{43} - 87530497425399433935056 q^{44} + 20184717117508544921875 q^{45} - 19156861509095148953472 q^{46} - 124130104426076147775874 q^{47} + 392740294920263915658112 q^{48} + 165605232197235024311237 q^{49} + 12466311454772949218750 q^{50} - 283285565607591290253932 q^{51} + 134524850423334877646616 q^{52} - 35755733205570847086718 q^{53} + 205572233114834325458800 q^{54} - 89257161400234375000000 q^{55} + 25462805189875911194400 q^{56} - 1319401932116898669671800 q^{57} - 579438611074148155852300 q^{58} - 1585020777269074637759500 q^{59} + 297498170171757812500000 q^{60} + 1111320149802275698049498 q^{61} + 9670161558160491301860192 q^{62} - 1904557057336614537087978 q^{63} + 1097697787230508110215232 q^{64} - 4324641710706691894531250 q^{65} - 4605695457765635004111424 q^{66} - 10660827150588937541043314 q^{67} - 25270829453141227103804792 q^{68} + 19102215953647051928319156 q^{69} + 532746949061894531250000 q^{70} + 30694868291812470499233628 q^{71} - 7743459253802850738963000 q^{72} + 34613217724841106415198562 q^{73} + 20863759039673808690243124 q^{74} + 3571632504463195800781250 q^{75} - 158372155959861065143050000 q^{76} + 27627355436868451222388832 q^{77} + 257928640210879380181789264 q^{78} - 57360196045020259089199400 q^{79} + 14769168824075175781250000 q^{80} + 61360230776764805612376829 q^{81} - 105697817457938588324666788 q^{82} - 405489941236272124736804598 q^{83} - 166720982995247714339423616 q^{84} + 19720379783776140136718750 q^{85} + 94968436265370679940316248 q^{86} + 175296011162333752897403900 q^{87} - 17617154500722062015364000 q^{88} + 690669510701840412130097850 q^{89} - 524497485154158986816406250 q^{90} + 321048736848260112206548988 q^{91} - 1567063632707439653869151664 q^{92} + 487024511594791002056522184 q^{93} + 1167880798538308416872749744 q^{94} - 522124553168604614257812500 q^{95} + 1560035816911548054960067328 q^{96} + 208777539760204460560475826 q^{97} + 749116677127114786688193838 q^{98} - 795772654946301078229652224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_0(5))\) 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
5.28.a.a 5.a 1.a $4$ $23.093$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-11550\) \(-2473800\) \(4882812500\) \(-215015185000\) $-$ $\mathrm{SU}(2)$ \(q+(-2887+\beta _{1})q^{2}+(-618547-195\beta _{1}+\cdots)q^{3}+\cdots\)
5.28.a.b 5.a 1.a $5$ $23.093$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(19916\) \(4870682\) \(-6103515625\) \(155646348206\) $+$ $\mathrm{SU}(2)$ \(q+(3983-\beta _{1})q^{2}+(974132-24\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{28}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{28}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{28}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)