Properties

Label 3584.2.a
Level $3584$
Weight $2$
Character orbit 3584.a
Rep. character $\chi_{3584}(1,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $16$
Sturm bound $1024$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(1024\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3584))\).

Total New Old
Modular forms 544 96 448
Cusp forms 481 96 385
Eisenstein series 63 0 63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(22\)
\(+\)\(-\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(26\)
\(-\)\(-\)\(+\)\(18\)
Plus space\(+\)\(40\)
Minus space\(-\)\(56\)

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \) \( 96 q + 96 q^{9} + 96 q^{25} + 96 q^{49} + 64 q^{65} + 64 q^{73} + 96 q^{81} + 64 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3584))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
3584.2.a.a 3584.a 1.a $2$ $28.618$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{7}-q^{9}-\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.a.b 3584.a 1.a $2$ $28.618$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{7}-q^{9}-\beta q^{11}-\beta q^{19}+\cdots\)
3584.2.a.c 3584.a 1.a $4$ $28.618$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.d 3584.a 1.a $4$ $28.618$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.e 3584.a 1.a $6$ $28.618$ 6.6.18857984.1 None \(0\) \(-4\) \(0\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.f 3584.a 1.a $6$ $28.618$ 6.6.18857984.1 None \(0\) \(-4\) \(0\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.g 3584.a 1.a $6$ $28.618$ 6.6.12836864.1 None \(0\) \(0\) \(-4\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.h 3584.a 1.a $6$ $28.618$ 6.6.12836864.1 None \(0\) \(0\) \(-4\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.i 3584.a 1.a $6$ $28.618$ 6.6.12836864.1 None \(0\) \(0\) \(4\) \(-6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.j 3584.a 1.a $6$ $28.618$ 6.6.12836864.1 None \(0\) \(0\) \(4\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{5})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.k 3584.a 1.a $6$ $28.618$ 6.6.18857984.1 None \(0\) \(4\) \(0\) \(-6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.l 3584.a 1.a $6$ $28.618$ 6.6.18857984.1 None \(0\) \(4\) \(0\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3584.2.a.m 3584.a 1.a $8$ $28.618$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{7}q^{3}+(-\beta _{3}-\beta _{7})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
3584.2.a.n 3584.a 1.a $8$ $28.618$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{7}q^{3}+(\beta _{3}+\beta _{7})q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3584.2.a.o 3584.a 1.a $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(-10\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}-\beta _{3}q^{5}-q^{7}+(2+\beta _{6})q^{9}+\cdots\)
3584.2.a.p 3584.a 1.a $10$ $28.618$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(10\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}+\beta _{3}q^{5}+q^{7}+(2+\beta _{6})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3584))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3584)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1792))\)\(^{\oplus 2}\)