Properties

Label 98.4.c
Level $98$
Weight $4$
Character orbit 98.c
Rep. character $\chi_{98}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $8$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(98, [\chi])\).

Total New Old
Modular forms 100 20 80
Cusp forms 68 20 48
Eisenstein series 32 0 32

Trace form

\( 20q - 6q^{3} - 40q^{4} - 2q^{5} + 16q^{6} - 168q^{9} + O(q^{10}) \) \( 20q - 6q^{3} - 40q^{4} - 2q^{5} + 16q^{6} - 168q^{9} - 32q^{10} - 30q^{11} - 24q^{12} + 8q^{13} - 68q^{15} - 160q^{16} + 110q^{17} + 40q^{18} + 142q^{19} + 16q^{20} + 512q^{22} + 26q^{23} - 32q^{24} - 520q^{25} - 272q^{26} - 396q^{27} - 824q^{29} + 264q^{30} + 98q^{31} + 250q^{33} + 32q^{34} + 1344q^{36} + 874q^{37} - 264q^{38} + 1604q^{39} - 128q^{40} + 1080q^{41} - 1272q^{43} - 120q^{44} - 164q^{45} + 248q^{46} + 30q^{47} + 192q^{48} - 2720q^{50} - 250q^{51} - 16q^{52} - 150q^{53} + 184q^{54} - 1516q^{55} + 1908q^{57} + 480q^{58} + 202q^{59} + 136q^{60} - 658q^{61} + 208q^{62} + 1280q^{64} + 1540q^{65} + 640q^{66} - 986q^{67} + 440q^{68} + 676q^{69} + 2288q^{71} + 160q^{72} - 18q^{73} - 1280q^{74} + 296q^{75} - 1136q^{76} - 2432q^{78} - 3078q^{79} - 32q^{80} - 1150q^{81} + 912q^{82} - 688q^{83} + 3236q^{85} - 1256q^{86} - 676q^{87} - 1024q^{88} - 1890q^{89} - 800q^{90} - 208q^{92} - 5210q^{93} + 744q^{94} + 1142q^{95} - 128q^{96} + 4248q^{97} - 6560q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
98.4.c.a \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-5\) \(-9\) \(0\) \(q-2\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.b \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-2\) \(-12\) \(0\) \(q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.c \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(-2\) \(2\) \(12\) \(0\) \(q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.d \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(2\) \(-8\) \(14\) \(0\) \(q+2\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.e \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(7\) \(0\) \(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.f \(2\) \(5.782\) \(\Q(\sqrt{-3}) \) None \(2\) \(8\) \(-14\) \(0\) \(q+2\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
98.4.c.g \(4\) \(5.782\) \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-2-2\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots\)
98.4.c.h \(4\) \(5.782\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(0\) \(0\) \(q+(2+2\beta _{2})q^{2}+(5\beta _{1}+5\beta _{3})q^{3}+4\beta _{2}q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)