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Properties

Label 4.48.a
Level $4$
Weight $48$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 48 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{48}(\Gamma_0(4))\).

Total New Old
Modular forms 25 4 21
Cusp forms 22 4 18
Eisenstein series 3 0 3

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

\(2\)Dim
\(-\)\(4\)

Trace form

\( 4 q + 127448165040 q^{3} - 23542166804473800 q^{5} - 90993274484744645920 q^{7} + 56321932207761182525076 q^{9} + O(q^{10}) \) \( 4 q + 127448165040 q^{3} - 23542166804473800 q^{5} - 90993274484744645920 q^{7} + 56321932207761182525076 q^{9} - 823485172346993530289520 q^{11} + 195465212601377598336943640 q^{13} - 1114065279181089484863343200 q^{15} - 99785600022823770860335089720 q^{17} + 488497552615114121294273142896 q^{19} - 19204931044253698447804681163136 q^{21} - 22323983900204520128774038289760 q^{23} - 291457545248137841903687107422500 q^{25} + 8035453829980412673741253598139360 q^{27} - 28487706447855813474853849811615784 q^{29} + 102528502733186256313953385188278144 q^{31} - 477522622647434367482957041776125760 q^{33} - 705228690249908700803487640268683200 q^{35} + 5647902254204183778250597161348488120 q^{37} + 14344095548001764381508646314996926496 q^{39} - 87429456988693406592963735241650629016 q^{41} - 151840903493312624535947925202592784880 q^{43} + 109228416671091235785027764415630283800 q^{45} - 2443612498745517874350155208548056132800 q^{47} + 1368734109510917819192865368033738935332 q^{49} - 39570089247370312319936101700601652950432 q^{51} - 57101933621097849473307058511962893930120 q^{53} - 218652629516151012749156864196834973908000 q^{55} - 817136559896322752719078696973392266237120 q^{57} - 994292166603047095087596479071896510382128 q^{59} - 3641524954708024405556731108517350381855912 q^{61} - 13052485194976682615837985935438087413495200 q^{63} - 15817286916470725439073193320314877584218800 q^{65} - 25075688367127492437123447111644230367628880 q^{67} - 60585641956584830998063328480873833511025792 q^{69} - 41936567649842792478325832429017860893318688 q^{71} - 55459113316618116275541750552935098048078360 q^{73} - 1575356777082551915299167743087309374590000 q^{75} + 705678334148373981318049274696504957378336640 q^{77} + 644673103282112983982537243943753779736552128 q^{79} + 3336263294773393431668200525444905762454715556 q^{81} + 4401620969097714516708833798553950893040338800 q^{83} + 5741597050746384822821388297005030210936847600 q^{85} + 5094367170275008062016959397743797210200692000 q^{87} + 4293102147826653455488766703494049055873679784 q^{89} - 6991510008310526419783143382637504193053015744 q^{91} - 30755976949434759003759996609627766515607426560 q^{93} - 63555038657191765010790706150061366872359967200 q^{95} - 137213861061009897031877298371917527101223666040 q^{97} - 388749156034904449887040774600210297410164197680 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{48}^{\mathrm{new}}(\Gamma_0(4))\) 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
4.48.a.a 4.a 1.a $4$ $55.963$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 4.48.a.a \(0\) \(127448165040\) \(-23\!\cdots\!00\) \(-90\!\cdots\!20\) $-$ $\mathrm{SU}(2)$ \(q+(31862041260-\beta _{1})q^{3}+(-5885541701118450+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{48}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{48}^{\mathrm{old}}(\Gamma_0(4)) \simeq \) \(S_{48}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{48}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)