Properties

Label 1470.2.d
Level $1470$
Weight $2$
Character orbit 1470.d
Rep. character $\chi_{1470}(1469,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $8$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(672\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

\( 80q + 80q^{4} + 4q^{9} + O(q^{10}) \) \( 80q + 80q^{4} + 4q^{9} + 4q^{15} + 80q^{16} + 4q^{25} + 4q^{30} + 4q^{36} + 56q^{39} + 40q^{46} + 40q^{51} + 4q^{60} + 80q^{64} + 8q^{79} - 92q^{81} - 56q^{85} - 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1470.2.d.a \(4\) \(11.738\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(-1\) \(3\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1470.2.d.b \(4\) \(11.738\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(1\) \(-3\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1470.2.d.c \(4\) \(11.738\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(-1\) \(-3\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
1470.2.d.d \(4\) \(11.738\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(1\) \(3\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots\)
1470.2.d.e \(8\) \(11.738\) 8.0.3317760000.3 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1470.2.d.f \(8\) \(11.738\) 8.0.3317760000.3 None \(8\) \(0\) \(0\) \(0\) \(q+q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1470.2.d.g \(24\) \(11.738\) None \(-24\) \(0\) \(0\) \(0\)
1470.2.d.h \(24\) \(11.738\) None \(24\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)