Properties

Label 5040.2.t
Level $5040$
Weight $2$
Character orbit 5040.t
Rep. character $\chi_{5040}(1009,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $28$
Sturm bound $2304$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(2304\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5040, [\chi])\).

Total New Old
Modular forms 1200 90 1110
Cusp forms 1104 90 1014
Eisenstein series 96 0 96

Trace form

\( 90q + 2q^{5} + O(q^{10}) \) \( 90q + 2q^{5} + 12q^{11} - 8q^{19} + 2q^{25} - 4q^{29} + 8q^{31} - 4q^{41} - 90q^{49} - 40q^{55} - 12q^{61} - 40q^{71} - 28q^{79} - 8q^{85} + 20q^{89} - 12q^{91} + 32q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5040, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5040.2.t.a \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}-iq^{7}-q^{11}-iq^{13}+\cdots\)
5040.2.t.b \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}-iq^{7}-4iq^{13}-2iq^{17}+\cdots\)
5040.2.t.c \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2+i)q^{5}-iq^{7}+4iq^{13}+2iq^{17}+\cdots\)
5040.2.t.d \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}+iq^{7}+4q^{11}+2iq^{13}+\cdots\)
5040.2.t.e \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+2i)q^{5}-iq^{7}-6q^{11}-2iq^{13}+\cdots\)
5040.2.t.f \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}+iq^{7}-2q^{11}-2iq^{13}+\cdots\)
5040.2.t.g \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}-iq^{7}-4iq^{13}-4iq^{17}+\cdots\)
5040.2.t.h \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}-iq^{7}+2q^{11}+6iq^{13}+\cdots\)
5040.2.t.i \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-2i)q^{5}-iq^{7}+6q^{11}+2iq^{13}+\cdots\)
5040.2.t.j \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}-iq^{7}-6q^{11}+2iq^{13}+\cdots\)
5040.2.t.k \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}+iq^{7}-2q^{11}+2iq^{13}+\cdots\)
5040.2.t.l \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1-2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots\)
5040.2.t.m \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots\)
5040.2.t.n \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+2i)q^{5}+iq^{7}+2q^{11}-2iq^{13}+\cdots\)
5040.2.t.o \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}-iq^{7}-4q^{11}+6iq^{13}+\cdots\)
5040.2.t.p \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+iq^{7}-3q^{11}-iq^{13}+\cdots\)
5040.2.t.q \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}+iq^{7}+4iq^{13}-2iq^{17}+\cdots\)
5040.2.t.r \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2+i)q^{5}+iq^{7}-4iq^{13}+2iq^{17}+\cdots\)
5040.2.t.s \(2\) \(40.245\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}+iq^{7}+3q^{11}+iq^{13}+\cdots\)
5040.2.t.t \(4\) \(40.245\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-1-\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
5040.2.t.u \(4\) \(40.245\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}-2q^{11}+2\beta _{2}q^{13}+\cdots\)
5040.2.t.v \(6\) \(40.245\) 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{2}q^{5}+\beta _{1}q^{7}+2q^{11}+(2\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
5040.2.t.w \(6\) \(40.245\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{1}q^{7}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
5040.2.t.x \(6\) \(40.245\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+\beta _{1}q^{7}+(2-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
5040.2.t.y \(6\) \(40.245\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{5}-\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
5040.2.t.z \(6\) \(40.245\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
5040.2.t.ba \(6\) \(40.245\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{11}+\cdots\)
5040.2.t.bb \(8\) \(40.245\) 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{5}+\beta _{1}q^{7}+(\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2520, [\chi])\)\(^{\oplus 2}\)