Properties

Label 75.4.b
Level $75$
Weight $4$
Character orbit 75.b
Rep. character $\chi_{75}(49,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $40$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 75.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(75, [\chi])\).

Total New Old
Modular forms 36 8 28
Cusp forms 24 8 16
Eisenstein series 12 0 12

Trace form

\( 8q - 36q^{4} - 24q^{6} - 72q^{9} + O(q^{10}) \) \( 8q - 36q^{4} - 24q^{6} - 72q^{9} + 112q^{11} - 324q^{14} + 180q^{16} + 276q^{19} - 108q^{21} + 468q^{24} - 764q^{26} - 488q^{29} + 68q^{31} + 1088q^{34} + 324q^{36} + 204q^{39} + 1688q^{41} + 712q^{44} - 2232q^{46} - 1100q^{49} - 816q^{51} + 216q^{54} - 480q^{56} - 496q^{59} + 2340q^{61} - 3284q^{64} + 1488q^{66} - 504q^{69} + 416q^{71} - 1904q^{74} + 784q^{76} + 3280q^{79} + 648q^{81} - 936q^{84} - 1508q^{86} - 984q^{89} - 2492q^{91} + 824q^{94} - 2748q^{96} - 1008q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.4.b.a \(2\) \(4.425\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{2}+3iq^{3}-q^{4}-9q^{6}+20iq^{7}+\cdots\)
75.4.b.b \(2\) \(4.425\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}-24iq^{7}+\cdots\)
75.4.b.c \(4\) \(4.425\) \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(-12+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)