Properties

Label 75.2.b
Level $75$
Weight $2$
Character orbit 75.b
Rep. character $\chi_{75}(49,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $20$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 75.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(75, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 4 4 0
Eisenstein series 12 0 12

Trace form

\( 4 q - 2 q^{4} - 2 q^{6} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{4} - 2 q^{6} - 4 q^{9} - 4 q^{11} + 12 q^{14} - 10 q^{16} + 2 q^{19} + 6 q^{21} + 6 q^{24} + 8 q^{26} - 16 q^{29} - 6 q^{31} - 4 q^{34} + 2 q^{36} - 2 q^{39} + 4 q^{41} - 16 q^{44} + 24 q^{46} + 10 q^{49} - 8 q^{51} + 2 q^{54} + 28 q^{59} + 10 q^{61} + 2 q^{64} - 16 q^{66} + 12 q^{69} - 32 q^{71} - 28 q^{74} - 28 q^{76} + 4 q^{81} - 12 q^{84} - 4 q^{86} + 12 q^{89} - 6 q^{91} + 8 q^{94} + 26 q^{96} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.2.b.a 75.b 5.b $2$ $0.599$ \(\Q(\sqrt{-1}) \) None 75.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots\)
75.2.b.b 75.b 5.b $2$ $0.599$ \(\Q(\sqrt{-1}) \) None 15.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)