Properties

Label 575.2.b
Level $575$
Weight $2$
Character orbit 575.b
Rep. character $\chi_{575}(24,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $6$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

Total New Old
Modular forms 66 34 32
Cusp forms 54 34 20
Eisenstein series 12 0 12

Trace form

\( 34q - 36q^{4} + 4q^{6} - 30q^{9} + O(q^{10}) \) \( 34q - 36q^{4} + 4q^{6} - 30q^{9} - 8q^{11} + 4q^{14} + 40q^{16} - 4q^{19} + 8q^{21} - 8q^{24} - 24q^{26} - 16q^{29} + 20q^{31} - 4q^{34} + 24q^{36} + 48q^{41} + 52q^{44} + 4q^{46} - 66q^{49} + 16q^{51} + 36q^{54} - 80q^{56} - 12q^{59} + 60q^{61} - 60q^{64} - 16q^{66} - 8q^{69} - 20q^{71} - 28q^{74} + 28q^{76} - 8q^{79} + 34q^{81} + 68q^{84} - 68q^{86} - 56q^{89} - 24q^{91} - 60q^{94} - 140q^{96} + 116q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
575.2.b.a \(2\) \(4.591\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots\)
575.2.b.b \(2\) \(4.591\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots\)
575.2.b.c \(4\) \(4.591\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
575.2.b.d \(4\) \(4.591\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
575.2.b.e \(8\) \(4.591\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
575.2.b.f \(14\) \(4.591\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)