Properties

Label 49.4.c
Level $49$
Weight $4$
Character orbit 49.c
Rep. character $\chi_{49}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $5$
Sturm bound $18$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(49, [\chi])\).

Total New Old
Modular forms 36 24 12
Cusp forms 20 16 4
Eisenstein series 16 8 8

Trace form

\( 16q + 3q^{2} + 7q^{3} - 33q^{4} + 7q^{5} - 28q^{6} + 54q^{8} + 11q^{9} + O(q^{10}) \) \( 16q + 3q^{2} + 7q^{3} - 33q^{4} + 7q^{5} - 28q^{6} + 54q^{8} + 11q^{9} + 14q^{10} - 11q^{11} - 28q^{12} + 28q^{13} - 158q^{15} + 19q^{16} - 21q^{17} + 145q^{18} + 49q^{19} + 56q^{20} + 12q^{22} - 249q^{23} - 168q^{24} + 67q^{25} - 28q^{26} + 70q^{27} - 136q^{29} + 390q^{30} + 147q^{31} + 277q^{32} - 35q^{33} + 84q^{34} - 550q^{36} - 389q^{37} + 98q^{38} - 742q^{39} - 168q^{40} - 700q^{41} + 984q^{43} + 564q^{44} + 154q^{45} - 482q^{46} + 525q^{47} + 224q^{48} + 3154q^{50} - 65q^{51} + 56q^{52} - 585q^{53} - 70q^{54} + 70q^{55} - 2202q^{57} - 386q^{58} - 105q^{59} + 812q^{60} - 413q^{61} - 588q^{62} - 3702q^{64} - 42q^{65} - 70q^{66} + 1781q^{67} + 84q^{68} + 2226q^{69} + 1936q^{71} - 267q^{72} - 1113q^{73} + 1604q^{74} - 532q^{75} + 392q^{76} - 2856q^{78} + 1655q^{79} - 112q^{80} + 524q^{81} + 700q^{82} - 2184q^{83} - 3406q^{85} - 5216q^{86} + 406q^{87} - 4200q^{88} - 329q^{89} - 616q^{90} + 5592q^{92} + 4387q^{93} + 1050q^{94} + 985q^{95} + 1120q^{96} + 1764q^{97} + 10868q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
49.4.c.a \(2\) \(2.891\) \(\Q(\sqrt{-3}) \) None \(-2\) \(7\) \(7\) \(0\) \(q-2\zeta_{6}q^{2}+(7-7\zeta_{6})q^{3}+(4-4\zeta_{6})q^{4}+\cdots\)
49.4.c.b \(2\) \(2.891\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(16\) \(0\) \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.c \(2\) \(2.891\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-16\) \(0\) \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
49.4.c.d \(2\) \(2.891\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) \(q+5\zeta_{6}q^{2}+(-17+17\zeta_{6})q^{4}-45q^{8}+\cdots\)
49.4.c.e \(8\) \(2.891\) 8.0.\(\cdots\).19 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2}-\beta _{6})q^{2}+\beta _{3}q^{3}+(-8+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

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