Properties

Label 2520.2.t
Level $2520$
Weight $2$
Character orbit 2520.t
Rep. character $\chi_{2520}(1009,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $11$
Sturm bound $1152$
Trace bound $19$

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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.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(1152\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 608 44 564
Cusp forms 544 44 500
Eisenstein series 64 0 64

Trace form

\( 44q + 4q^{5} + O(q^{10}) \) \( 44q + 4q^{5} - 12q^{11} - 8q^{25} - 28q^{29} - 8q^{31} + 16q^{41} - 44q^{49} + 32q^{55} + 24q^{59} + 16q^{61} + 24q^{65} + 4q^{79} - 4q^{85} - 24q^{89} + 12q^{91} - 20q^{95} + O(q^{100}) \)

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.t.a \(2\) \(20.122\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}+iq^{7}+q^{11}-iq^{13}+\cdots\)
2520.2.t.b \(2\) \(20.122\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+2i)q^{5}+iq^{7}+2q^{11}+2iq^{13}+\cdots\)
2520.2.t.c \(2\) \(20.122\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots\)
2520.2.t.d \(2\) \(20.122\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots\)
2520.2.t.e \(2\) \(20.122\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}-iq^{7}-2q^{11}-2iq^{13}+\cdots\)
2520.2.t.f \(4\) \(20.122\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}+2q^{11}-2\beta _{2}q^{13}+\cdots\)
2520.2.t.g \(6\) \(20.122\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2520.2.t.h \(6\) \(20.122\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}-\beta _{1}q^{7}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
2520.2.t.i \(6\) \(20.122\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{5}+\beta _{1}q^{7}+(2-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.t.j \(6\) \(20.122\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
2520.2.t.k \(6\) \(20.122\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)