Properties

Label 3584.2.m
Level $3584$
Weight $2$
Character orbit 3584.m
Rep. character $\chi_{3584}(897,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Newform subspaces $40$
Sturm bound $1024$
Trace bound $35$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 40 \)
Sturm bound: \(1024\)
Trace bound: \(35\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3584, [\chi])\).

Total New Old
Modular forms 1088 192 896
Cusp forms 960 192 768
Eisenstein series 128 0 128

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 192 q^{49} - 128 q^{65} - 192 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3584.2.m.a 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+(-1-i)q^{5}+iq^{7}+\cdots\)
3584.2.m.b 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2i)q^{3}+(1+i)q^{5}-iq^{7}+\cdots\)
3584.2.m.c 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.d 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.e 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.f 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.g 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
3584.2.m.h 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}-iq^{7}+iq^{9}+(2+2i)q^{11}+\cdots\)
3584.2.m.i 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2+2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.j 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2+2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.k 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2+2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.l 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(2+2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.m 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{5}+iq^{7}+3iq^{9}+(-4+\cdots)q^{11}+\cdots\)
3584.2.m.n 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{5}-iq^{7}+3iq^{9}+(4+4i)q^{11}+\cdots\)
3584.2.m.o 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{5}-iq^{7}+3iq^{9}+(-4-4i)q^{11}+\cdots\)
3584.2.m.p 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{5}+iq^{7}+3iq^{9}+(4+4i)q^{11}+\cdots\)
3584.2.m.q 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.r 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.s 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2-2i)q^{5}+iq^{7}+\cdots\)
3584.2.m.t 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
3584.2.m.u 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}-iq^{7}+iq^{9}+(-2-2i)q^{11}+\cdots\)
3584.2.m.v 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+iq^{7}+iq^{9}+(-2-2i)q^{11}+\cdots\)
3584.2.m.w 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2+2i)q^{5}-iq^{7}+iq^{9}+\cdots\)
3584.2.m.x 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2+2i)q^{5}+iq^{7}+iq^{9}+\cdots\)
3584.2.m.y 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2+2i)q^{5}-iq^{7}+iq^{9}+\cdots\)
3584.2.m.z 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(2+2i)q^{5}+iq^{7}+iq^{9}+\cdots\)
3584.2.m.ba 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(-1-i)q^{5}-iq^{7}+\cdots\)
3584.2.m.bb 3584.m 16.e $2$ $28.618$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(1+i)q^{5}+iq^{7}-5iq^{9}+\cdots\)
3584.2.m.bc 3584.m 16.e $4$ $28.618$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bd 3584.m 16.e $4$ $28.618$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.be 3584.m 16.e $4$ $28.618$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bf 3584.m 16.e $4$ $28.618$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
3584.2.m.bg 3584.m 16.e $6$ $28.618$ 6.0.399424.1 None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(-1-\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)
3584.2.m.bh 3584.m 16.e $6$ $28.618$ 6.0.399424.1 None \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots\)
3584.2.m.bi 3584.m 16.e $6$ $28.618$ 6.0.399424.1 None \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
3584.2.m.bj 3584.m 16.e $6$ $28.618$ 6.0.399424.1 None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
3584.2.m.bk 3584.m 16.e $24$ $28.618$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
3584.2.m.bl 3584.m 16.e $24$ $28.618$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
3584.2.m.bm 3584.m 16.e $24$ $28.618$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
3584.2.m.bn 3584.m 16.e $24$ $28.618$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)