Properties

Label 75.3.d
Level $75$
Weight $3$
Character orbit 75.d
Rep. character $\chi_{75}(74,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $30$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(75, [\chi])\).

Total New Old
Modular forms 26 14 12
Cusp forms 14 10 4
Eisenstein series 12 4 8

Trace form

\( 10q + 24q^{4} - 2q^{6} - 28q^{9} + O(q^{10}) \) \( 10q + 24q^{4} - 2q^{6} - 28q^{9} - 24q^{16} + 54q^{19} - 18q^{21} - 126q^{24} + 70q^{31} + 4q^{34} - 22q^{36} + 22q^{39} - 144q^{46} + 104q^{49} - 62q^{51} + 212q^{54} + 390q^{61} - 352q^{64} + 470q^{66} + 252q^{69} - 484q^{76} - 316q^{79} - 380q^{81} + 312q^{84} - 406q^{91} - 176q^{94} + 14q^{96} - 710q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.3.d.a \(2\) \(2.044\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-4q^{4}+11iq^{7}-9q^{9}-12iq^{12}+\cdots\)
75.3.d.b \(4\) \(2.044\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(5-\beta _{2}+\cdots)q^{6}+\cdots\)
75.3.d.c \(4\) \(2.044\) \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+7q^{4}+(-6+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)