Properties

Label 7200.2.f
Level $7200$
Weight $2$
Character orbit 7200.f
Rep. character $\chi_{7200}(6049,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $37$
Sturm bound $2880$
Trace bound $49$

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Defining parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(2880\)
Trace bound: \(49\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7200, [\chi])\).

Total New Old
Modular forms 1536 90 1446
Cusp forms 1344 90 1254
Eisenstein series 192 0 192

Trace form

\( 90q + O(q^{10}) \) \( 90q + 20q^{29} + 28q^{41} - 122q^{49} - 4q^{61} - 76q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7200.2.f.a \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-5q^{11}+5iq^{17}-5q^{19}+\cdots\)
7200.2.f.b \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4q^{11}+iq^{13}-iq^{17}-8q^{19}+\cdots\)
7200.2.f.c \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-4q^{11}+3iq^{13}+iq^{17}+\cdots\)
7200.2.f.d \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}-3iq^{13}-4iq^{17}+\cdots\)
7200.2.f.e \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-4q^{11}-7iq^{13}+4iq^{17}+\cdots\)
7200.2.f.f \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-4q^{11}-iq^{13}-3iq^{17}+\cdots\)
7200.2.f.g \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}+3iq^{13}-iq^{17}+\cdots\)
7200.2.f.h \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}+iq^{17}-4q^{19}+2q^{29}+\cdots\)
7200.2.f.i \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}+iq^{17}+4q^{19}-2q^{29}+\cdots\)
7200.2.f.j \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-5iq^{13}-5q^{19}-4iq^{23}+\cdots\)
7200.2.f.k \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{13}-3iq^{17}-4q^{19}-4iq^{23}+\cdots\)
7200.2.f.l \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-iq^{13}-3q^{19}+4iq^{23}+\cdots\)
7200.2.f.m \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{13}+iq^{17}-10q^{29}+iq^{37}+\cdots\)
7200.2.f.n \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{13}+4iq^{17}-4q^{29}+iq^{37}+\cdots\)
7200.2.f.o \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-iq^{13}-3iq^{17}+2iq^{23}+\cdots\)
7200.2.f.p \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+iq^{13}+3iq^{17}+2iq^{23}+\cdots\)
7200.2.f.q \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{13}-4iq^{17}+4q^{29}+iq^{37}+\cdots\)
7200.2.f.r \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+iq^{13}+3q^{19}+4iq^{23}+\cdots\)
7200.2.f.s \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{13}+3iq^{17}+4q^{19}-4iq^{23}+\cdots\)
7200.2.f.t \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+5iq^{13}+5q^{19}-4iq^{23}+\cdots\)
7200.2.f.u \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-iq^{17}-4q^{19}-2q^{29}+\cdots\)
7200.2.f.v \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-iq^{17}+4q^{19}+2q^{29}+\cdots\)
7200.2.f.w \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+4q^{11}-3iq^{13}+iq^{17}+\cdots\)
7200.2.f.x \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}+iq^{13}+3iq^{17}+\cdots\)
7200.2.f.y \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+4q^{11}+7iq^{13}-4iq^{17}+\cdots\)
7200.2.f.z \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+4q^{11}+3iq^{13}+4iq^{17}+\cdots\)
7200.2.f.ba \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}-3iq^{13}-iq^{17}+\cdots\)
7200.2.f.bb \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{11}+iq^{13}-iq^{17}+8q^{19}+\cdots\)
7200.2.f.bc \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+5q^{11}-5iq^{17}+5q^{19}+\cdots\)
7200.2.f.bd \(4\) \(57.492\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}-2q^{11}-3\beta _{1}q^{13}-2\beta _{2}q^{17}+\cdots\)
7200.2.f.be \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-\beta _{3}q^{11}-2\beta _{1}q^{13}-\beta _{1}q^{17}+\cdots\)
7200.2.f.bf \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-2\beta _{3}q^{11}-\beta _{1}q^{13}+2\beta _{1}q^{17}+\cdots\)
7200.2.f.bg \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{7}+\beta _{3}q^{11}+4\beta _{1}q^{13}-7\beta _{1}q^{17}+\cdots\)
7200.2.f.bh \(4\) \(57.492\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-\zeta_{8}q^{13}+\zeta_{8}q^{17}+\cdots\)
7200.2.f.bi \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+2\beta _{3}q^{11}-\beta _{1}q^{13}-2\beta _{1}q^{17}+\cdots\)
7200.2.f.bj \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+\beta _{3}q^{11}-2\beta _{1}q^{13}+\beta _{1}q^{17}+\cdots\)
7200.2.f.bk \(4\) \(57.492\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}+2q^{11}-3\beta _{1}q^{13}+2\beta _{2}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3600, [\chi])\)\(^{\oplus 2}\)