Properties

Label 25.10
Level 25
Weight 10
Dimension 197
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 500
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(500\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(25))\).

Total New Old
Modular forms 239 218 21
Cusp forms 211 197 14
Eisenstein series 28 21 7

Trace form

\( 197q + 26q^{2} - 302q^{3} + 1534q^{4} - 1775q^{5} + 3214q^{6} - 11894q^{7} + 25190q^{8} - 14904q^{9} + O(q^{10}) \) \( 197q + 26q^{2} - 302q^{3} + 1534q^{4} - 1775q^{5} + 3214q^{6} - 11894q^{7} + 25190q^{8} - 14904q^{9} + 70400q^{10} - 175506q^{11} - 454314q^{12} + 1818q^{13} + 1797638q^{14} + 162960q^{15} - 4022898q^{16} - 305894q^{17} - 607622q^{18} + 1635350q^{19} + 5586410q^{20} - 4174266q^{21} - 4763738q^{22} - 155382q^{23} - 7528340q^{24} - 7141265q^{25} - 6581316q^{26} + 13939210q^{27} + 30852022q^{28} + 11741490q^{29} - 18521930q^{30} + 1252894q^{31} - 28564554q^{32} + 7870806q^{33} - 28518802q^{34} - 1807960q^{35} + 40796982q^{36} + 15309381q^{37} + 114225260q^{38} + 3597222q^{39} - 147465460q^{40} - 5397866q^{41} - 29250758q^{42} - 28065862q^{43} + 236348968q^{44} + 252763505q^{45} + 141597994q^{46} - 95150894q^{47} - 474300012q^{48} - 147164151q^{49} - 296219950q^{50} - 182418336q^{51} - 70041084q^{52} + 295474253q^{53} + 1088861840q^{54} + 311889870q^{55} - 393637550q^{56} - 482446090q^{57} - 351622780q^{58} + 46871130q^{59} - 120766990q^{60} + 168620734q^{61} + 274492272q^{62} - 14922322q^{63} - 1443524136q^{64} - 1598125945q^{65} - 876432082q^{66} + 689769226q^{67} + 3225529382q^{68} + 2419745542q^{69} + 1881992270q^{70} + 530670374q^{71} - 1562593080q^{72} - 2049558102q^{73} - 6631076892q^{74} - 2916728540q^{75} + 253548420q^{76} + 1921698582q^{77} + 3361105976q^{78} + 2614262070q^{79} + 5408991110q^{80} + 1790266452q^{81} + 2935692102q^{82} + 781861398q^{83} - 3457426522q^{84} - 4035826615q^{85} - 2723757126q^{86} - 8104003990q^{87} - 8306215810q^{88} + 1920727575q^{89} + 11577233550q^{90} + 5775589774q^{91} + 9208664226q^{92} + 4750859686q^{93} + 4533024518q^{94} + 248605210q^{95} - 5295840886q^{96} - 8831007394q^{97} - 10373469818q^{98} - 6760099788q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
25.10.a \(\chi_{25}(1, \cdot)\) 25.10.a.a 1 1
25.10.a.b 2
25.10.a.c 3
25.10.a.d 3
25.10.a.e 4
25.10.b \(\chi_{25}(24, \cdot)\) 25.10.b.a 2 1
25.10.b.b 4
25.10.b.c 6
25.10.d \(\chi_{25}(6, \cdot)\) 25.10.d.a 84 4
25.10.e \(\chi_{25}(4, \cdot)\) 25.10.e.a 88 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)