Properties

Label 289.10.a
Level $289$
Weight $10$
Character orbit 289.a
Rep. character $\chi_{289}(1,\cdot)$
Character field $\Q$
Dimension $196$
Newform subspaces $9$
Sturm bound $255$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(255\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(289))\).

Total New Old
Modular forms 238 211 27
Cusp forms 220 196 24
Eisenstein series 18 15 3

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

\(17\)Dim.
\(+\)\(96\)
\(-\)\(100\)

Trace form

\( 196q + 34q^{2} + 148q^{3} + 47958q^{4} - 2842q^{5} + 4142q^{6} + 3814q^{7} + 25602q^{8} + 1167312q^{9} + O(q^{10}) \) \( 196q + 34q^{2} + 148q^{3} + 47958q^{4} - 2842q^{5} + 4142q^{6} + 3814q^{7} + 25602q^{8} + 1167312q^{9} - 64898q^{10} - 67500q^{11} + 207850q^{12} + 10812q^{13} - 362552q^{14} + 428808q^{15} + 10244814q^{16} + 1529134q^{18} - 181288q^{19} - 715478q^{20} + 1106564q^{21} + 1100230q^{22} - 3003634q^{23} - 1191342q^{24} + 65253928q^{25} + 15482240q^{26} + 7517332q^{27} + 3145520q^{28} - 4635618q^{29} + 1043358q^{30} + 3715622q^{31} - 7350732q^{32} + 3741768q^{33} + 27291512q^{35} + 214045756q^{36} + 13124210q^{37} + 22147432q^{38} - 43856988q^{39} - 73224598q^{40} - 2288748q^{41} + 43544174q^{42} + 17308040q^{43} - 140019678q^{44} - 121715946q^{45} + 183572956q^{46} - 31987948q^{47} + 304192994q^{48} + 902842108q^{49} + 275535184q^{50} + 1113008q^{52} - 97649496q^{53} - 292953820q^{54} - 143391872q^{55} - 121233936q^{56} - 290228864q^{57} + 172256422q^{58} + 60328920q^{59} + 874804850q^{60} + 127601298q^{61} - 251348744q^{62} + 194130634q^{63} + 2271192898q^{64} + 162954956q^{65} + 154507016q^{66} + 5267144q^{67} + 1640756q^{69} - 1036203924q^{70} - 175871018q^{71} + 466746800q^{72} - 16675856q^{73} - 511462886q^{74} - 765386140q^{75} + 766416100q^{76} - 114390484q^{77} - 1015080612q^{78} - 130907274q^{79} - 220577342q^{80} + 5491482932q^{81} + 63174400q^{82} + 1324473876q^{83} - 1528687596q^{84} - 1419305638q^{86} + 1870991644q^{87} - 114058870q^{88} + 1652886404q^{89} + 4524752134q^{90} + 866519200q^{91} - 3407899844q^{92} - 2809301340q^{93} + 144343396q^{94} + 1750951648q^{95} + 1506989058q^{96} - 2698561500q^{97} + 1512014884q^{98} + 552052864q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(289))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
289.10.a.a \(5\) \(148.845\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(236\) \(-1480\) \(13202\) \(+\) \(q+(-7+\beta _{1})q^{2}+(48-2\beta _{1}-\beta _{4})q^{3}+\cdots\)
289.10.a.b \(7\) \(148.845\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(-88\) \(-1362\) \(-9388\) \(+\) \(q-\beta _{1}q^{2}+(-12-2\beta _{1}+\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)
289.10.a.c \(12\) \(148.845\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-30\) \(0\) \(0\) \(0\) \(+\) \(q+(-2+\beta _{2})q^{2}-\beta _{1}q^{3}+(154-4\beta _{2}+\cdots)q^{4}+\cdots\)
289.10.a.d \(12\) \(148.845\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(17\) \(-74\) \(-454\) \(5524\) \(+\) \(q+(1+\beta _{1})q^{2}+(-6+\beta _{3})q^{3}+(249+\cdots)q^{4}+\cdots\)
289.10.a.e \(12\) \(148.845\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(17\) \(74\) \(454\) \(-5524\) \(-\) \(q+(1+\beta _{1})q^{2}+(6-\beta _{3})q^{3}+(249-\beta _{1}+\cdots)q^{4}+\cdots\)
289.10.a.f \(24\) \(148.845\) None \(0\) \(0\) \(0\) \(0\) \(+\)
289.10.a.g \(36\) \(148.845\) None \(0\) \(-486\) \(-3750\) \(-29040\) \(+\)
289.10.a.h \(36\) \(148.845\) None \(0\) \(486\) \(3750\) \(29040\) \(-\)
289.10.a.i \(52\) \(148.845\) None \(64\) \(0\) \(0\) \(0\) \(-\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(289))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(289)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)