Properties

Label 2520.2.bi
Level $2520$
Weight $2$
Character orbit 2520.bi
Rep. character $\chi_{2520}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $19$
Sturm bound $1152$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(1152\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

Total New Old
Modular forms 1216 80 1136
Cusp forms 1088 80 1008
Eisenstein series 128 0 128

Trace form

\( 80q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 80q + 2q^{5} - 4q^{7} + 2q^{11} + 12q^{17} + 6q^{19} - 40q^{25} - 20q^{29} - 8q^{31} - 2q^{35} - 4q^{37} + 16q^{41} - 12q^{47} - 42q^{49} - 20q^{53} - 4q^{59} - 14q^{61} - 6q^{65} + 12q^{67} + 64q^{71} - 4q^{73} + 48q^{77} + 56q^{83} + 26q^{89} + 28q^{91} - 4q^{95} + 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2520.2.bi.a \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-5\) \(q-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.b \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
2520.2.bi.c \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.d \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.e \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2520.2.bi.f \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(5\) \(q-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2520.2.bi.g \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-5\) \(q+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}-q^{13}+(2+\cdots)q^{17}+\cdots\)
2520.2.bi.h \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
2520.2.bi.i \(2\) \(20.122\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2520.2.bi.j \(4\) \(20.122\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.k \(4\) \(20.122\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(2\) \(-2\) \(q-\beta _{2}q^{5}+(-1-\beta _{1}-\beta _{2}-2\beta _{3})q^{7}+\cdots\)
2520.2.bi.l \(4\) \(20.122\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(2\) \(-2\) \(q-\beta _{2}q^{5}+(\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\beta _{1}q^{11}+\cdots\)
2520.2.bi.m \(6\) \(20.122\) 6.0.4406832.1 None \(0\) \(0\) \(-3\) \(-1\) \(q+(-1+\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.bi.n \(6\) \(20.122\) 6.0.29428272.1 None \(0\) \(0\) \(-3\) \(0\) \(q+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.o \(6\) \(20.122\) 6.0.38363328.2 None \(0\) \(0\) \(3\) \(-2\) \(q-\beta _{3}q^{5}+(-\beta _{1}+\beta _{4})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.bi.p \(6\) \(20.122\) 6.0.4406832.1 None \(0\) \(0\) \(3\) \(-1\) \(q+(1-\beta _{4})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.bi.q \(6\) \(20.122\) 6.0.11337408.1 None \(0\) \(0\) \(3\) \(6\) \(q+\beta _{2}q^{5}+(1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots\)
2520.2.bi.r \(10\) \(20.122\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-5\) \(-1\) \(q+\beta _{1}q^{5}+\beta _{6}q^{7}+\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)
2520.2.bi.s \(10\) \(20.122\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(5\) \(-1\) \(q-\beta _{1}q^{5}+\beta _{6}q^{7}-\beta _{3}q^{11}+(\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)