Properties

Label 154.4.a
Level $154$
Weight $4$
Character orbit 154.a
Rep. character $\chi_{154}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $9$
Sturm bound $96$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(154))\).

Total New Old
Modular forms 76 14 62
Cusp forms 68 14 54
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.

\(2\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
Plus space\(+\)\(9\)
Minus space\(-\)\(5\)

Trace form

\( 14 q + 4 q^{2} - 8 q^{3} + 56 q^{4} + 36 q^{5} + 16 q^{8} + 154 q^{9} + O(q^{10}) \) \( 14 q + 4 q^{2} - 8 q^{3} + 56 q^{4} + 36 q^{5} + 16 q^{8} + 154 q^{9} - 8 q^{10} - 22 q^{11} - 32 q^{12} + 76 q^{13} - 56 q^{14} + 52 q^{15} + 224 q^{16} - 60 q^{17} + 164 q^{18} - 80 q^{19} + 144 q^{20} - 44 q^{22} + 100 q^{23} + 246 q^{25} - 112 q^{26} - 68 q^{27} + 140 q^{29} + 272 q^{30} - 52 q^{31} + 64 q^{32} + 352 q^{33} + 680 q^{34} + 112 q^{35} + 616 q^{36} + 232 q^{37} - 168 q^{38} - 728 q^{39} - 32 q^{40} - 1196 q^{41} - 168 q^{42} - 280 q^{43} - 88 q^{44} - 736 q^{45} - 320 q^{46} - 504 q^{47} - 128 q^{48} + 686 q^{49} + 1452 q^{50} - 2024 q^{51} + 304 q^{52} - 596 q^{53} - 1200 q^{54} + 792 q^{55} - 224 q^{56} - 2240 q^{57} + 1496 q^{58} + 880 q^{59} + 208 q^{60} + 548 q^{61} - 688 q^{62} + 840 q^{63} + 896 q^{64} + 1120 q^{65} - 84 q^{67} - 240 q^{68} - 652 q^{69} - 280 q^{70} - 1508 q^{71} + 656 q^{72} + 468 q^{73} + 728 q^{74} + 308 q^{75} - 320 q^{76} - 308 q^{77} + 1264 q^{78} - 2552 q^{79} + 576 q^{80} + 1454 q^{81} - 3224 q^{82} - 3664 q^{83} - 3616 q^{85} - 736 q^{86} - 2936 q^{87} - 176 q^{88} + 3088 q^{89} - 2456 q^{90} + 476 q^{91} + 400 q^{92} - 68 q^{93} - 1520 q^{94} + 1232 q^{95} - 608 q^{97} + 196 q^{98} - 154 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(154))\) 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 7 11
154.4.a.a 154.a 1.a $1$ $9.086$ \(\Q\) None \(-2\) \(-5\) \(-1\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}+4q^{4}-q^{5}+10q^{6}+\cdots\)
154.4.a.b 154.a 1.a $1$ $9.086$ \(\Q\) None \(-2\) \(0\) \(2\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+2q^{5}-7q^{7}-8q^{8}+\cdots\)
154.4.a.c 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(-10\) \(-14\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-10q^{3}+4q^{4}-14q^{5}-20q^{6}+\cdots\)
154.4.a.d 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(-2\) \(18\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots\)
154.4.a.e 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(7\) \(3\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}+4q^{4}+3q^{5}+14q^{6}+\cdots\)
154.4.a.f 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{137}) \) None \(-4\) \(-5\) \(-7\) \(14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
154.4.a.g 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{37}) \) None \(-4\) \(6\) \(26\) \(14\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots\)
154.4.a.h 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{57}) \) None \(4\) \(-5\) \(-17\) \(-14\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots\)
154.4.a.i 154.a 1.a $3$ $9.086$ 3.3.7636.1 None \(6\) \(6\) \(26\) \(-21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(154)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)