Properties

Label 1680.2.t
Level $1680$
Weight $2$
Character orbit 1680.t
Rep. character $\chi_{1680}(1009,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $11$
Sturm bound $768$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(768\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1680, [\chi])\).

Total New Old
Modular forms 408 36 372
Cusp forms 360 36 324
Eisenstein series 48 0 48

Trace form

\( 36q - 4q^{5} - 36q^{9} + O(q^{10}) \) \( 36q - 4q^{5} - 36q^{9} - 8q^{19} - 4q^{25} + 8q^{29} + 8q^{31} + 16q^{39} + 8q^{41} + 4q^{45} - 36q^{49} + 32q^{51} - 40q^{55} - 24q^{61} + 16q^{65} + 16q^{69} - 16q^{75} + 32q^{79} + 36q^{81} - 8q^{85} - 40q^{89} + 24q^{91} - 64q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1680.2.t.a \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}+(-2-i)q^{5}-iq^{7}-q^{9}+\cdots\)
1680.2.t.b \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+2i)q^{5}+iq^{7}-q^{9}+\cdots\)
1680.2.t.c \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-2i)q^{5}+iq^{7}-q^{9}+\cdots\)
1680.2.t.d \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots\)
1680.2.t.e \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+(1+2i)q^{5}-iq^{7}-q^{9}-2q^{11}+\cdots\)
1680.2.t.f \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+6q^{11}+\cdots\)
1680.2.t.g \(2\) \(13.415\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{3}+(2-i)q^{5}-iq^{7}-q^{9}-4q^{11}+\cdots\)
1680.2.t.h \(4\) \(13.415\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}+2q^{11}+\cdots\)
1680.2.t.i \(6\) \(13.415\) 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1680.2.t.j \(6\) \(13.415\) 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
1680.2.t.k \(6\) \(13.415\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)