Properties

Label 3150.2.d
Level 3150
Weight 2
Character orbit d
Rep. character \(\chi_{3150}(3149,\cdot)\)
Character field \(\Q\)
Dimension 48
Newforms 6
Sturm bound 1440
Trace bound 13

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1440\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 768 48 720
Cusp forms 672 48 624
Eisenstein series 96 0 96

Trace form

\(48q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut +\mathstrut 48q^{4} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 48q^{64} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut +\mathstrut 64q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3150.2.d.a \(8\) \(25.153\) 8.0.7442857984.4 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.b \(8\) \(25.153\) 8.0.40960000.1 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{7}-q^{8}+\beta _{2}q^{11}+\cdots\)
3150.2.d.c \(8\) \(25.153\) 8.0.7442857984.4 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.d \(8\) \(25.153\) 8.0.7442857984.4 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.e \(8\) \(25.153\) 8.0.40960000.1 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+q^{8}+\beta _{2}q^{11}+\cdots\)
3150.2.d.f \(8\) \(25.153\) 8.0.7442857984.4 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)