Properties

Label 48.24.a
Level $48$
Weight $24$
Character orbit 48.a
Rep. character $\chi_{48}(1,\cdot)$
Character field $\Q$
Dimension $23$
Newform subspaces $12$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 48.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(48))\).

Total New Old
Modular forms 190 23 167
Cusp forms 178 23 155
Eisenstein series 12 0 12

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.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(11\)

Trace form

\( 23 q - 177147 q^{3} - 35553398 q^{5} + 27593280 q^{7} + 721764371007 q^{9} + O(q^{10}) \) \( 23 q - 177147 q^{3} - 35553398 q^{5} + 27593280 q^{7} + 721764371007 q^{9} - 975574266676 q^{11} - 5284814079046 q^{13} + 17299511718750 q^{15} - 56302527224626 q^{17} - 700384900299820 q^{19} + 5921082022875464 q^{23} + 57717463712682481 q^{25} - 5559060566555523 q^{27} - 778581049687374 q^{29} + 316791945163282232 q^{31} + 236459885057021988 q^{33} + 219175960478184576 q^{35} - 1533016585964591838 q^{37} + 1681155442695099438 q^{39} - 3652830720208460346 q^{41} + 2684315834380626508 q^{43} - 1115703301940501382 q^{45} - 33778365706201587840 q^{47} + 99538549563390988111 q^{49} - 62346681209313931158 q^{51} - 96398147486913285206 q^{53} + 322208100589453929928 q^{55} + 89919149506187253948 q^{57} + 63500437084458904460 q^{59} - 117617946959802242086 q^{61} + 865906364487827520 q^{63} - 206092062639310512548 q^{65} - 445234951699067987692 q^{67} + 870236643724638946776 q^{69} - 3056895351026800555976 q^{71} - 512153577805261992970 q^{73} - 1459093771454659607277 q^{75} + 6527914323198865251840 q^{77} + 9794012917997409828808 q^{79} + 22649730750223058356263 q^{81} - 10059806789290426358828 q^{83} - 6256603404868382193452 q^{85} + 44628647451580554808662 q^{87} - 17769723919775888095194 q^{89} - 53557681244953177200768 q^{91} + 20709005626086325284456 q^{93} - 242915750516448472512008 q^{95} + 21513078783188928101614 q^{97} - 30614554215566018289684 q^{99} + O(q^{100}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(48))\) 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
48.24.a.a 48.a 1.a $1$ $160.898$ \(\Q\) None \(0\) \(-177147\) \(-48863730\) \(1723688680\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}-48863730q^{5}+1723688680q^{7}+\cdots\)
48.24.a.b 48.a 1.a $1$ $160.898$ \(\Q\) None \(0\) \(-177147\) \(-35483250\) \(2385847912\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}-35483250q^{5}+2385847912q^{7}+\cdots\)
48.24.a.c 48.a 1.a $1$ $160.898$ \(\Q\) None \(0\) \(177147\) \(-9019770\) \(-515282432\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}-9019770q^{5}-515282432q^{7}+\cdots\)
48.24.a.d 48.a 1.a $1$ $160.898$ \(\Q\) None \(0\) \(177147\) \(196251270\) \(8131131904\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}+196251270q^{5}+8131131904q^{7}+\cdots\)
48.24.a.e 48.a 1.a $2$ $160.898$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-354294\) \(25248156\) \(-5764462768\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}+(12624078-\beta )q^{5}+(-2882231384+\cdots)q^{7}+\cdots\)
48.24.a.f 48.a 1.a $2$ $160.898$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(-354294\) \(73907100\) \(1531228496\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}+(36953550-\beta )q^{5}+(765614248+\cdots)q^{7}+\cdots\)
48.24.a.g 48.a 1.a $2$ $160.898$ \(\Q(\sqrt{530401}) \) None \(0\) \(354294\) \(-46808820\) \(211963904\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}+(-23404410-245\beta )q^{5}+\cdots\)
48.24.a.h 48.a 1.a $2$ $160.898$ \(\Q(\sqrt{1792561}) \) None \(0\) \(354294\) \(-34222068\) \(-21634816\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}+(-17111034-19\beta )q^{5}+\cdots\)
48.24.a.i 48.a 1.a $2$ $160.898$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(0\) \(354294\) \(2075980\) \(-4451754048\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}+(1037990-5\beta )q^{5}+(-2225877024+\cdots)q^{7}+\cdots\)
48.24.a.j 48.a 1.a $3$ $160.898$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-531441\) \(-45012150\) \(-281292072\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}+(-15004050-\beta _{1})q^{5}+\cdots\)
48.24.a.k 48.a 1.a $3$ $160.898$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-531441\) \(-36400950\) \(418786392\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3^{11}q^{3}+(-12133650-\beta _{1})q^{5}+\cdots\)
48.24.a.l 48.a 1.a $3$ $160.898$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(531441\) \(-77225166\) \(-3340627872\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3^{11}q^{3}+(-25741722+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(48)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)