Properties

Label 2448.4.a
Level $2448$
Weight $4$
Character orbit 2448.a
Rep. character $\chi_{2448}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $49$
Sturm bound $1728$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2448.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 49 \)
Sturm bound: \(1728\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2448))\).

Total New Old
Modular forms 1320 120 1200
Cusp forms 1272 120 1152
Eisenstein series 48 0 48

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

\(2\)\(3\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(-\)\(+\)$-$\(17\)
\(+\)\(-\)\(-\)$+$\(19\)
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(12\)
\(-\)\(-\)\(+\)$+$\(19\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(62\)
Minus space\(-\)\(58\)

Trace form

\( 120 q - 22 q^{7} + O(q^{10}) \) \( 120 q - 22 q^{7} + 46 q^{11} - 180 q^{19} - 302 q^{23} + 2832 q^{25} - 144 q^{29} + 66 q^{31} + 228 q^{35} - 8 q^{37} + 296 q^{41} - 668 q^{43} - 1368 q^{47} + 6752 q^{49} + 376 q^{53} + 612 q^{55} + 1020 q^{59} - 744 q^{65} - 1440 q^{67} - 1734 q^{71} + 768 q^{73} + 624 q^{77} + 2614 q^{79} + 1340 q^{83} + 248 q^{89} + 984 q^{91} - 4728 q^{95} + 440 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2448))\) 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 17
2448.4.a.a 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-17\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-17q^{5}-6q^{7}-17q^{11}+43q^{13}+\cdots\)
2448.4.a.b 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-16\) \(-34\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}-34q^{7}-48q^{11}+58q^{13}+\cdots\)
2448.4.a.c 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-16\) \(-24\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}-24q^{7}+62q^{11}-62q^{13}+\cdots\)
2448.4.a.d 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-9\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-9q^{5}+10q^{7}-15q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.e 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-6\) \(24\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-6q^{5}+24q^{7}+44q^{11}+6q^{13}+\cdots\)
2448.4.a.f 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-6\) \(28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-6q^{5}+28q^{7}-24q^{11}-58q^{13}+\cdots\)
2448.4.a.g 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(-5\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}-12q^{7}+37q^{11}+19q^{13}+\cdots\)
2448.4.a.h 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(3\) \(-20\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-20q^{7}-51q^{11}-61q^{13}+\cdots\)
2448.4.a.i 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(3\) \(16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+2^{4}q^{7}-57q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.j 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(5\) \(32\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+2^{5}q^{7}+3^{3}q^{11}-69q^{13}+\cdots\)
2448.4.a.k 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(7\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+7q^{5}-4q^{7}-21q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.l 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(8\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{5}+12q^{7}-10q^{11}-38q^{13}+\cdots\)
2448.4.a.m 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(9\) \(10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+9q^{5}+10q^{7}+15q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.n 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(10\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+10q^{5}+8q^{7}+12q^{11}-26q^{13}+\cdots\)
2448.4.a.o 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(12\) \(22\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+12q^{5}+22q^{7}-48q^{11}+2q^{13}+\cdots\)
2448.4.a.p 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(17\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+17q^{5}-6q^{7}+17q^{11}+43q^{13}+\cdots\)
2448.4.a.q 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(18\) \(10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+18q^{5}+10q^{7}-6q^{11}+74q^{13}+\cdots\)
2448.4.a.r 2448.a 1.a $1$ $144.437$ \(\Q\) None \(0\) \(0\) \(20\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+20q^{5}+2q^{7}-48q^{11}-14q^{13}+\cdots\)
2448.4.a.s 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{217}) \) None \(0\) \(0\) \(-19\) \(-18\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-9-\beta )q^{5}+(-8-2\beta )q^{7}+(9-3\beta )q^{11}+\cdots\)
2448.4.a.t 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{15}) \) None \(0\) \(0\) \(-12\) \(-16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta )q^{5}+(-8-\beta )q^{7}+(-12+\cdots)q^{11}+\cdots\)
2448.4.a.u 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{241}) \) None \(0\) \(0\) \(-7\) \(-18\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{5}+(-8-2\beta )q^{7}+(9+3\beta )q^{11}+\cdots\)
2448.4.a.v 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta )q^{5}+(4-\beta )q^{7}+(33+\beta )q^{11}+\cdots\)
2448.4.a.w 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{393}) \) None \(0\) \(0\) \(-3\) \(-22\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-12+2\beta )q^{7}+(1+\cdots)q^{11}+\cdots\)
2448.4.a.x 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{201}) \) None \(0\) \(0\) \(-3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+2\beta q^{7}+(-5-5\beta )q^{11}+\cdots\)
2448.4.a.y 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(4\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+4\beta )q^{5}+(3+\beta )q^{7}+(-3+15\beta )q^{11}+\cdots\)
2448.4.a.z 2448.a 1.a $2$ $144.437$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(12\) \(36\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(6+2\beta )q^{5}+(18+3\beta )q^{7}+(-10+\cdots)q^{11}+\cdots\)
2448.4.a.ba 2448.a 1.a $3$ $144.437$ 3.3.1524.1 None \(0\) \(0\) \(-26\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-9+\beta _{1})q^{5}+(-2-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bb 2448.a 1.a $3$ $144.437$ 3.3.2747992.1 None \(0\) \(0\) \(-25\) \(-18\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-8-\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bc 2448.a 1.a $3$ $144.437$ 3.3.104664.1 None \(0\) \(0\) \(-19\) \(10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-6-\beta _{1})q^{5}+(2+4\beta _{1}-\beta _{2})q^{7}+\cdots\)
2448.4.a.bd 2448.a 1.a $3$ $144.437$ 3.3.5912.1 None \(0\) \(0\) \(-8\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{5}+(2+3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.be 2448.a 1.a $3$ $144.437$ 3.3.23321.1 None \(0\) \(0\) \(-5\) \(-20\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{5}+(-7+\beta _{1})q^{7}+(9+\cdots)q^{11}+\cdots\)
2448.4.a.bf 2448.a 1.a $3$ $144.437$ 3.3.1556.1 None \(0\) \(0\) \(-2\) \(-12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+(-4+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2448.4.a.bg 2448.a 1.a $3$ $144.437$ 3.3.12821.1 None \(0\) \(0\) \(4\) \(-28\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-2\beta _{2})q^{5}+(-9-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bh 2448.a 1.a $3$ $144.437$ 3.3.4481.1 None \(0\) \(0\) \(5\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{1})q^{7}+(2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bi 2448.a 1.a $3$ $144.437$ 3.3.2636.1 None \(0\) \(0\) \(8\) \(-22\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{2})q^{5}+(-8+\beta _{1}+2\beta _{2})q^{7}+\cdots\)
2448.4.a.bj 2448.a 1.a $3$ $144.437$ 3.3.8396.1 None \(0\) \(0\) \(8\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1}+2\beta _{2})q^{5}+(2+3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bk 2448.a 1.a $3$ $144.437$ 3.3.17717.1 None \(0\) \(0\) \(10\) \(22\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{5}+(8-\beta _{1}+\beta _{2})q^{7}+(-11+\cdots)q^{11}+\cdots\)
2448.4.a.bl 2448.a 1.a $3$ $144.437$ 3.3.21324.1 None \(0\) \(0\) \(19\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(7+\beta _{1}-\beta _{2})q^{5}+(3-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
2448.4.a.bm 2448.a 1.a $3$ $144.437$ 3.3.104664.1 None \(0\) \(0\) \(19\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(6+\beta _{1})q^{5}+(2+4\beta _{1}-\beta _{2})q^{7}+(14+\cdots)q^{11}+\cdots\)
2448.4.a.bn 2448.a 1.a $3$ $144.437$ 3.3.2747992.1 None \(0\) \(0\) \(25\) \(-18\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(8+\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(-2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bo 2448.a 1.a $4$ $144.437$ 4.4.1506848.1 None \(0\) \(0\) \(-22\) \(24\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-5+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.bp 2448.a 1.a $4$ $144.437$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-10\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2448.4.a.bq 2448.a 1.a $4$ $144.437$ 4.4.550476.1 None \(0\) \(0\) \(-8\) \(22\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(4+2\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.br 2448.a 1.a $4$ $144.437$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(2\) \(-32\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+(-9-\beta _{1}+\beta _{2})q^{7}+(15+\cdots)q^{11}+\cdots\)
2448.4.a.bs 2448.a 1.a $4$ $144.437$ 4.4.1506848.1 None \(0\) \(0\) \(22\) \(24\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(5-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.bt 2448.a 1.a $5$ $144.437$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(0\) \(-13\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{3})q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
2448.4.a.bu 2448.a 1.a $5$ $144.437$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(0\) \(13\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{3})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)
2448.4.a.bv 2448.a 1.a $7$ $144.437$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-3\) \(-26\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{5}+(-4-\beta _{3})q^{7}+(9+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bw 2448.a 1.a $7$ $144.437$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(3\) \(-26\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{5}+(-4-\beta _{3})q^{7}+(-9-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2448))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2448)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 2}\)