Properties

Label 6030.2.d
Level 6030
Weight 2
Character orbit d
Rep. character \(\chi_{6030}(2411,\cdot)\)
Character field \(\Q\)
Dimension 96
Newforms 12
Sturm bound 2448
Trace bound 11

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Defining parameters

Level: \( N \) = \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6030.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(2448\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6030, [\chi])\).

Total New Old
Modular forms 1240 96 1144
Cusp forms 1208 96 1112
Eisenstein series 32 0 32

Trace form

\(96q \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(96q \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut 96q^{16} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 96q^{25} \) \(\mathstrut -\mathstrut 48q^{37} \) \(\mathstrut -\mathstrut 144q^{49} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut -\mathstrut 56q^{67} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 64q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6030, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6030.2.d.a \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-6q^{11}+\cdots\)
6030.2.d.b \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+q^{5}+2\beta q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.c \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
6030.2.d.d \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+q^{5}+\beta q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.e \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.f \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
6030.2.d.g \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-q^{5}+2\beta q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.h \(2\) \(48.150\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+6q^{11}+\cdots\)
6030.2.d.i \(16\) \(48.150\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(16\) \(0\) \(q-q^{2}+q^{4}+q^{5}+\beta _{12}q^{7}-q^{8}-q^{10}+\cdots\)
6030.2.d.j \(16\) \(48.150\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(-16\) \(0\) \(q+q^{2}+q^{4}-q^{5}+\beta _{12}q^{7}+q^{8}-q^{10}+\cdots\)
6030.2.d.k \(24\) \(48.150\) None \(-24\) \(0\) \(-24\) \(0\)
6030.2.d.l \(24\) \(48.150\) None \(24\) \(0\) \(24\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(6030, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6030, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(603, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1206, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3015, [\chi])\)\(^{\oplus 2}\)