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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

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.2.b.a \(2\) \(0.599\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots\)
75.2.b.b \(2\) \(0.599\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)