Properties

Label 4680.2.l
Level $4680$
Weight $2$
Character orbit 4680.l
Rep. character $\chi_{4680}(2809,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $11$
Sturm bound $2016$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4680.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(2016\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4680, [\chi])\).

Total New Old
Modular forms 1040 90 950
Cusp forms 976 90 886
Eisenstein series 64 0 64

Trace form

\( 90 q + O(q^{10}) \) \( 90 q - 12 q^{11} - 12 q^{19} - 20 q^{25} - 12 q^{29} + 8 q^{31} - 2 q^{35} + 12 q^{41} - 78 q^{49} + 8 q^{55} + 76 q^{59} + 12 q^{61} - 8 q^{71} + 8 q^{79} - 44 q^{85} - 44 q^{89} + 12 q^{91} - 60 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4680, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4680.2.l.a \(2\) \(37.370\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+4iq^{7}+2q^{11}-iq^{13}+\cdots\)
4680.2.l.b \(2\) \(37.370\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}+iq^{7}-3q^{11}+iq^{13}+\cdots\)
4680.2.l.c \(2\) \(37.370\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}+5iq^{7}-5q^{11}+iq^{13}+\cdots\)
4680.2.l.d \(6\) \(37.370\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{7}+\cdots\)
4680.2.l.e \(6\) \(37.370\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{5}+(2-\beta _{4}-\beta _{5})q^{11}-\beta _{3}q^{13}+\cdots\)
4680.2.l.f \(8\) \(37.370\) 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{5}-\beta _{4}q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
4680.2.l.g \(8\) \(37.370\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
4680.2.l.h \(10\) \(37.370\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(-1+\beta _{4})q^{11}+\cdots\)
4680.2.l.i \(10\) \(37.370\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{2}q^{5}+\beta _{4}q^{7}+(-3+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
4680.2.l.j \(18\) \(37.370\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{13}+\cdots)q^{11}+\cdots\)
4680.2.l.k \(18\) \(37.370\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(1+\beta _{13}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2340, [\chi])\)\(^{\oplus 2}\)