Properties

Label 1470.2.m
Level $1470$
Weight $2$
Character orbit 1470.m
Rep. character $\chi_{1470}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $6$
Sturm bound $672$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(672\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 736 80 656
Cusp forms 608 80 528
Eisenstein series 128 0 128

Trace form

\( 80q + O(q^{10}) \) \( 80q - 16q^{11} + 8q^{15} - 80q^{16} - 24q^{22} - 48q^{23} - 16q^{30} - 80q^{36} + 64q^{37} + 16q^{43} + 16q^{46} - 32q^{51} - 80q^{53} + 16q^{57} - 56q^{58} + 64q^{65} - 32q^{67} - 32q^{78} - 80q^{81} - 80q^{85} - 32q^{86} + 24q^{88} - 48q^{92} + 16q^{93} + 16q^{95} + O(q^{100}) \)

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.m.a \(8\) \(11.738\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1470.2.m.b \(8\) \(11.738\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{3}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1470.2.m.c \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{6}q^{2}-\beta _{6}q^{3}-\beta _{5}q^{4}+\beta _{3}q^{5}+\cdots\)
1470.2.m.d \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}-\beta _{10}q^{3}-\beta _{8}q^{4}+(1+2\beta _{1}+\cdots)q^{5}+\cdots\)
1470.2.m.e \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}+\beta _{10}q^{3}-\beta _{8}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1470.2.m.f \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(8\) \(0\) \(q-\beta _{6}q^{2}+\beta _{6}q^{3}-\beta _{5}q^{4}-\beta _{3}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)