Properties

Label 525.2.g
Level 525
Weight 2
Character orbit g
Rep. character \(\chi_{525}(524,\cdot)\)
Character field \(\Q\)
Dimension 44
Newforms 6
Sturm bound 160
Trace bound 6

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(160\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 92 52 40
Cusp forms 68 44 24
Eisenstein series 24 8 16

Trace form

\(44q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(44q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut 40q^{16} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 88q^{46} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut -\mathstrut 60q^{51} \) \(\mathstrut -\mathstrut 32q^{64} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 112q^{81} \) \(\mathstrut -\mathstrut 36q^{84} \) \(\mathstrut +\mathstrut 54q^{91} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.2.g.a \(4\) \(4.192\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-2q^{4}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
525.2.g.b \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}-3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.c \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}+3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.d \(8\) \(4.192\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
525.2.g.e \(8\) \(4.192\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.2.g.f \(16\) \(4.192\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}-\beta _{8}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)