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Properties

Label 153.4.f
Level $153$
Weight $4$
Character orbit 153.f
Rep. character $\chi_{153}(55,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $3$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 153.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(153, [\chi])\).

Total New Old
Modular forms 116 48 68
Cusp forms 100 44 56
Eisenstein series 16 4 12

Trace form

\( 44 q - 180 q^{4} + 18 q^{5} + 2 q^{7} + O(q^{10}) \) \( 44 q - 180 q^{4} + 18 q^{5} + 2 q^{7} - 66 q^{10} + 12 q^{11} + 8 q^{13} + 180 q^{14} + 468 q^{16} - 6 q^{17} - 78 q^{20} - 186 q^{22} - 186 q^{23} + 28 q^{28} - 366 q^{29} - 590 q^{31} + 930 q^{34} + 12 q^{35} + 14 q^{37} + 936 q^{38} + 1314 q^{40} + 168 q^{41} - 678 q^{44} + 1600 q^{46} + 252 q^{50} - 2284 q^{52} - 2620 q^{55} - 1260 q^{56} - 1822 q^{58} + 214 q^{61} + 1980 q^{62} + 1900 q^{64} + 3660 q^{65} + 188 q^{67} - 1674 q^{68} - 2754 q^{71} - 712 q^{73} - 3810 q^{74} - 3982 q^{79} - 882 q^{80} - 5728 q^{82} + 3178 q^{85} + 1020 q^{86} + 6634 q^{88} + 4764 q^{89} + 4272 q^{91} + 6840 q^{92} - 1644 q^{95} - 1104 q^{97} - 5520 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(153, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
153.4.f.a 153.f 17.c $8$ $9.027$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-14\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-5-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
153.4.f.b 153.f 17.c $16$ $9.027$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(32\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(-4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
153.4.f.c 153.f 17.c $20$ $9.027$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}+(-5+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{13}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(153, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(153, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)