Properties

Label 7200.2.d
Level $7200$
Weight $2$
Character orbit 7200.d
Rep. character $\chi_{7200}(2449,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $21$
Sturm bound $2880$
Trace bound $53$

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Defining parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(2880\)
Trace bound: \(53\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(37\), \(41\), \(53\)

Dimensions

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

Total New Old
Modular forms 1536 92 1444
Cusp forms 1344 88 1256
Eisenstein series 192 4 188

Trace form

\( 88 q + O(q^{10}) \) \( 88 q - 72 q^{49} - 8 q^{71} - 40 q^{79} - 8 q^{89} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7200.2.d.a 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 360.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}-\beta q^{11}-6 q^{13}-3\beta q^{17}+\cdots\)
7200.2.d.b 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 360.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}+\beta q^{11}-6 q^{13}+3\beta q^{17}+\cdots\)
7200.2.d.c 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 200.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2 i q^{7}-5 i q^{11}-6 q^{13}-3 i q^{17}+\cdots\)
7200.2.d.d 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 24.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}-4 q^{13}+\beta q^{17}+2\beta q^{19}+\cdots\)
7200.2.d.e 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 120.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}-2\beta q^{11}-3\beta q^{17}-2\beta q^{19}+\cdots\)
7200.2.d.f 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 120.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}+2\beta q^{11}-3\beta q^{17}+2\beta q^{19}+\cdots\)
7200.2.d.g 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 24.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}+4 q^{13}+\beta q^{17}-2\beta q^{19}+\cdots\)
7200.2.d.h 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 360.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}+\beta q^{11}+6 q^{13}-3\beta q^{17}+\cdots\)
7200.2.d.i 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 360.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}-\beta q^{11}+6 q^{13}+3\beta q^{17}+\cdots\)
7200.2.d.j 7200.d 40.f $2$ $57.492$ \(\Q(\sqrt{-1}) \) None 200.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2 i q^{7}+5 i q^{11}+6 q^{13}-3 i q^{17}+\cdots\)
7200.2.d.k 7200.d 40.f $4$ $57.492$ \(\Q(i, \sqrt{7})\) None 360.2.k.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{7}-\beta _{1}q^{11}-\beta _{3}q^{19}-\beta _{3}q^{23}+\cdots\)
7200.2.d.l 7200.d 40.f $4$ $57.492$ \(\Q(i, \sqrt{7})\) None 360.2.k.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{7}+\beta _{1}q^{11}-\beta _{3}q^{19}+\beta _{3}q^{23}+\cdots\)
7200.2.d.m 7200.d 40.f $4$ $57.492$ \(\Q(i, \sqrt{7})\) None 200.2.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4\beta _{1}q^{7}+\beta _{3}q^{11}-3\beta _{1}q^{17}+\beta _{3}q^{19}+\cdots\)
7200.2.d.n 7200.d 40.f $4$ $57.492$ \(\Q(\zeta_{12})\) None 40.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{3} q^{7}+\beta_{2} q^{11}+2\beta_1 q^{13}+(-2\beta_{3}-\beta_{2})q^{17}+\cdots\)
7200.2.d.o 7200.d 40.f $4$ $57.492$ \(\Q(\zeta_{12})\) None 40.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{3} q^{7}-\beta_{2} q^{11}-2\beta_1 q^{13}+(-2\beta_{3}-\beta_{2})q^{17}+\cdots\)
7200.2.d.p 7200.d 40.f $4$ $57.492$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) 72.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta_1 q^{7}+2\beta_{2} q^{11}-\beta_{2} q^{29}+10 q^{31}+\cdots\)
7200.2.d.q 7200.d 40.f $6$ $57.492$ 6.0.399424.1 None 120.2.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{7}+(\beta _{2}-\beta _{3}-\beta _{5})q^{11}-\beta _{1}q^{13}+\cdots\)
7200.2.d.r 7200.d 40.f $6$ $57.492$ 6.0.399424.1 None 120.2.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{7}+(-\beta _{2}+\beta _{3}+\beta _{5})q^{11}+\beta _{1}q^{13}+\cdots\)
7200.2.d.s 7200.d 40.f $8$ $57.492$ 8.0.214798336.3 None 600.2.k.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{7})q^{7}-\beta _{5}q^{11}+(-\beta _{1}-\beta _{3}+\cdots)q^{13}+\cdots\)
7200.2.d.t 7200.d 40.f $8$ $57.492$ 8.0.214798336.3 None 600.2.k.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{7})q^{7}+\beta _{5}q^{11}+(\beta _{1}+\beta _{3}+\cdots)q^{13}+\cdots\)
7200.2.d.u 7200.d 40.f $16$ $57.492$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1800.2.k.r \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{7}+\beta _{4}q^{11}-\beta _{3}q^{13}+(\beta _{5}-\beta _{7}+\cdots)q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(7200, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)