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Properties

Label 154.4.e
Level $154$
Weight $4$
Character orbit 154.e
Rep. character $\chi_{154}(23,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $4$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(154, [\chi])\).

Total New Old
Modular forms 152 40 112
Cusp forms 136 40 96
Eisenstein series 16 0 16

Trace form

\( 40 q - 12 q^{3} - 80 q^{4} - 20 q^{5} - 16 q^{6} + 100 q^{7} - 208 q^{9} + O(q^{10}) \) \( 40 q - 12 q^{3} - 80 q^{4} - 20 q^{5} - 16 q^{6} + 100 q^{7} - 208 q^{9} - 48 q^{12} - 88 q^{13} - 176 q^{14} - 160 q^{15} - 320 q^{16} + 96 q^{17} - 16 q^{18} + 428 q^{19} + 160 q^{20} - 436 q^{21} - 72 q^{23} + 32 q^{24} - 628 q^{25} - 312 q^{26} - 744 q^{27} - 128 q^{28} - 328 q^{29} + 160 q^{30} + 472 q^{31} - 132 q^{33} + 304 q^{34} + 200 q^{35} + 1664 q^{36} - 1120 q^{37} - 280 q^{38} - 184 q^{39} + 568 q^{41} - 792 q^{42} + 1136 q^{43} - 1672 q^{45} + 264 q^{46} + 316 q^{47} + 384 q^{48} - 1088 q^{49} + 192 q^{50} - 1508 q^{51} + 176 q^{52} - 640 q^{53} + 1232 q^{54} + 352 q^{56} + 4056 q^{57} - 472 q^{58} - 1612 q^{59} + 320 q^{60} + 356 q^{61} + 1968 q^{62} + 1120 q^{63} + 2560 q^{64} + 2152 q^{65} - 528 q^{66} + 2196 q^{67} + 384 q^{68} - 192 q^{69} - 536 q^{70} + 6016 q^{71} - 64 q^{72} - 244 q^{73} - 888 q^{74} - 208 q^{75} - 3424 q^{76} + 176 q^{77} - 4064 q^{78} + 1972 q^{79} - 320 q^{80} - 1796 q^{81} + 400 q^{82} - 4992 q^{83} + 1904 q^{84} - 4352 q^{85} - 968 q^{86} + 2064 q^{87} - 836 q^{89} - 144 q^{90} + 2408 q^{91} + 576 q^{92} + 4316 q^{93} + 2352 q^{94} + 3324 q^{95} + 128 q^{96} + 9528 q^{97} + 4032 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(154, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.4.e.a 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-11\) \(-20\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{3}q^{2}+(-2+\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{3}+\cdots\)
154.4.e.b 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(7\) \(10\) \(62\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+(1-\beta _{1}+\beta _{4})q^{3}+(-4+\cdots)q^{4}+\cdots\)
154.4.e.c 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-7\) \(-20\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{6})q^{2}+(\beta _{1}-\beta _{2}+\beta _{6})q^{3}+\cdots\)
154.4.e.d 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(10\) \(48\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(154, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)