Properties

Label 153.4.a
Level $153$
Weight $4$
Character orbit 153.a
Rep. character $\chi_{153}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $9$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 153.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(153))\).

Total New Old
Modular forms 58 20 38
Cusp forms 50 20 30
Eisenstein series 8 0 8

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

\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(11\)
Minus space\(-\)\(9\)

Trace form

\( 20 q - 2 q^{2} + 90 q^{4} + 2 q^{5} - 46 q^{7} - 30 q^{8} + O(q^{10}) \) \( 20 q - 2 q^{2} + 90 q^{4} + 2 q^{5} - 46 q^{7} - 30 q^{8} + 22 q^{10} + 36 q^{11} + 76 q^{13} + 112 q^{14} + 298 q^{16} + 34 q^{17} + 60 q^{19} + 130 q^{20} - 434 q^{22} - 82 q^{23} + 496 q^{25} + 4 q^{26} - 168 q^{28} - 6 q^{29} - 702 q^{31} + 338 q^{32} - 68 q^{34} + 20 q^{35} - 318 q^{37} + 380 q^{38} + 542 q^{40} - 804 q^{41} + 848 q^{43} + 90 q^{44} - 284 q^{46} - 1032 q^{47} + 220 q^{49} - 862 q^{50} - 1784 q^{52} + 12 q^{53} - 908 q^{55} + 960 q^{56} + 1654 q^{58} - 816 q^{59} - 1982 q^{61} - 776 q^{62} + 3730 q^{64} + 596 q^{65} + 460 q^{67} + 408 q^{68} - 736 q^{70} + 3238 q^{71} - 2272 q^{73} - 914 q^{74} + 3344 q^{76} + 1104 q^{77} + 1666 q^{79} + 2434 q^{80} - 1568 q^{82} - 872 q^{83} - 578 q^{85} + 40 q^{86} - 6586 q^{88} + 1064 q^{89} + 1440 q^{91} - 4484 q^{92} - 696 q^{94} + 2800 q^{95} + 2356 q^{97} - 6042 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(153))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 17
153.4.a.a 153.a 1.a $1$ $9.027$ \(\Q\) None \(-1\) \(0\) \(10\) \(-8\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+10q^{5}-8q^{7}+15q^{8}+\cdots\)
153.4.a.b 153.a 1.a $1$ $9.027$ \(\Q\) None \(1\) \(0\) \(-16\) \(34\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}-2^{4}q^{5}+34q^{7}-15q^{8}+\cdots\)
153.4.a.c 153.a 1.a $1$ $9.027$ \(\Q\) None \(1\) \(0\) \(20\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}+20q^{5}-2q^{7}-15q^{8}+\cdots\)
153.4.a.d 153.a 1.a $1$ $9.027$ \(\Q\) None \(3\) \(0\) \(-6\) \(-28\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}-6q^{5}-28q^{7}-21q^{8}+\cdots\)
153.4.a.e 153.a 1.a $2$ $9.027$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+10q^{4}+(-3+4\beta )q^{5}+(-4+\cdots)q^{7}+\cdots\)
153.4.a.f 153.a 1.a $3$ $9.027$ 3.3.5912.1 None \(-5\) \(0\) \(-8\) \(-8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
153.4.a.g 153.a 1.a $3$ $9.027$ 3.3.2636.1 None \(-1\) \(0\) \(8\) \(22\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(8-3\beta _{1}-\beta _{2})q^{4}+\cdots\)
153.4.a.h 153.a 1.a $4$ $9.027$ 4.4.1506848.1 None \(-4\) \(0\) \(-22\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(6+2\beta _{2}-\beta _{3})q^{4}+\cdots\)
153.4.a.i 153.a 1.a $4$ $9.027$ 4.4.1506848.1 None \(4\) \(0\) \(22\) \(-24\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{2}+(6-2\beta _{2}-\beta _{3})q^{4}+(5+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(153))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(153)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)