Properties

Label 468.4.a
Level $468$
Weight $4$
Character orbit 468.a
Rep. character $\chi_{468}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $8$
Sturm bound $336$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 468.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(336\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(468))\).

Total New Old
Modular forms 264 15 249
Cusp forms 240 15 225
Eisenstein series 24 0 24

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

\(2\)\(3\)\(13\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(9\)
Minus space\(-\)\(6\)

Trace form

\( 15 q - 26 q^{5} - 8 q^{7} + O(q^{10}) \) \( 15 q - 26 q^{5} - 8 q^{7} + 56 q^{11} + 13 q^{13} + 120 q^{17} + 108 q^{19} - 44 q^{23} + 155 q^{25} - 122 q^{29} + 272 q^{31} + 22 q^{35} + 330 q^{37} - 114 q^{41} - 386 q^{43} + 896 q^{47} + 1377 q^{49} + 354 q^{53} + 1704 q^{55} - 188 q^{59} + 118 q^{61} - 52 q^{65} + 560 q^{67} + 632 q^{71} + 1626 q^{73} + 1208 q^{77} + 132 q^{79} - 1680 q^{83} + 1528 q^{85} + 150 q^{89} - 130 q^{91} + 444 q^{95} + 734 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(468))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13
468.4.a.a 468.a 1.a $1$ $27.613$ \(\Q\) None 156.4.a.b \(0\) \(0\) \(2\) \(-32\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2^{5}q^{7}+68q^{11}+13q^{13}+\cdots\)
468.4.a.b 468.a 1.a $1$ $27.613$ \(\Q\) None 156.4.a.a \(0\) \(0\) \(6\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+6q^{5}-4q^{7}-6^{2}q^{11}+13q^{13}+\cdots\)
468.4.a.c 468.a 1.a $1$ $27.613$ \(\Q\) None 52.4.a.a \(0\) \(0\) \(13\) \(-11\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+13q^{5}-11q^{7}+2q^{11}-13q^{13}+\cdots\)
468.4.a.d 468.a 1.a $2$ $27.613$ \(\Q(\sqrt{10}) \) None 156.4.a.d \(0\) \(0\) \(-24\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-12+\beta )q^{5}+(4+3\beta )q^{7}+(-18+\cdots)q^{11}+\cdots\)
468.4.a.e 468.a 1.a $2$ $27.613$ \(\Q(\sqrt{217}) \) None 52.4.a.b \(0\) \(0\) \(-23\) \(27\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-11-\beta )q^{5}+(13+\beta )q^{7}+(-2+\cdots)q^{11}+\cdots\)
468.4.a.f 468.a 1.a $2$ $27.613$ \(\Q(\sqrt{13}) \) None 468.4.a.f \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-2q^{7}+4\beta q^{11}-13q^{13}+\cdots\)
468.4.a.g 468.a 1.a $2$ $27.613$ \(\Q(\sqrt{22}) \) None 156.4.a.c \(0\) \(0\) \(0\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(4+3\beta )q^{7}+(30+2\beta )q^{11}+\cdots\)
468.4.a.h 468.a 1.a $4$ $27.613$ 4.4.5126992.1 None 468.4.a.h \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(\beta _{1}-\beta _{2})q^{11}+13q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(468))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(468)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)