Properties

Label 2304.2.a
Level $2304$
Weight $2$
Character orbit 2304.a
Rep. character $\chi_{2304}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $26$
Sturm bound $768$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(768\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2304))\).

Total New Old
Modular forms 432 42 390
Cusp forms 337 38 299
Eisenstein series 95 4 91

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(10\)
Plus space\(+\)\(16\)
Minus space\(-\)\(22\)

Trace form

\( 38 q + O(q^{10}) \) \( 38 q + 4 q^{17} + 34 q^{25} - 4 q^{41} + 54 q^{49} + 52 q^{73} + 12 q^{89} + 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2304))\) 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 3
2304.2.a.a 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-4q^{5}+4q^{13}+2q^{17}+11q^{25}+\cdots\)
2304.2.a.b 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.c 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}-4q^{13}+8q^{17}-q^{25}+10q^{29}+\cdots\)
2304.2.a.d 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}+4q^{13}-8q^{17}-q^{25}+10q^{29}+\cdots\)
2304.2.a.e 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.f 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.g 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.h 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-6q^{11}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
2304.2.a.i 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q+6q^{11}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
2304.2.a.j 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.k 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+4q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.l 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.m 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+2q^{5}-4q^{13}-8q^{17}-q^{25}-10q^{29}+\cdots\)
2304.2.a.n 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+2q^{5}+4q^{13}+8q^{17}-q^{25}-10q^{29}+\cdots\)
2304.2.a.o 2304.a 1.a $1$ $18.398$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.p 2304.a 1.a $1$ $18.398$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{5}-4q^{13}+2q^{17}+11q^{25}+\cdots\)
2304.2.a.q 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{5}-2q^{7}-2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots\)
2304.2.a.r 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{7}-4q^{11}+2\beta q^{13}+2q^{17}+\cdots\)
2304.2.a.s 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{7}-6q^{17}-4q^{19}-2\beta q^{23}+\cdots\)
2304.2.a.t 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{11}-6q^{17}-3\beta q^{19}-5q^{25}+\cdots\)
2304.2.a.u 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}-6q^{17}+4q^{19}+2\beta q^{23}+\cdots\)
2304.2.a.v 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{7}-2\beta q^{13}-8q^{19}-5q^{25}+\cdots\)
2304.2.a.w 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-\beta q^{7}-2\beta q^{13}+8q^{19}-5q^{25}+\cdots\)
2304.2.a.x 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+4q^{11}+2\beta q^{13}+2q^{17}+\cdots\)
2304.2.a.y 2304.a 1.a $2$ $18.398$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(4\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{5}+2q^{7}+2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots\)
2304.2.a.z 2304.a 1.a $4$ $18.398$ \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{11}+7q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2304))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2304)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 2}\)