Properties

Label 154.8.a
Level $154$
Weight $8$
Character orbit 154.a
Rep. character $\chi_{154}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $8$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 154.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(154))\).

Total New Old
Modular forms 172 34 138
Cusp forms 164 34 130
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
\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(5\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(19\)
Minus space\(-\)\(15\)

Trace form

\( 34 q - 16 q^{2} + 52 q^{3} + 2176 q^{4} - 64 q^{5} - 1024 q^{8} + 17554 q^{9} + O(q^{10}) \) \( 34 q - 16 q^{2} + 52 q^{3} + 2176 q^{4} - 64 q^{5} - 1024 q^{8} + 17554 q^{9} + 11552 q^{10} - 2662 q^{11} + 3328 q^{12} + 8276 q^{13} - 10976 q^{14} + 20992 q^{15} + 139264 q^{16} + 15444 q^{17} - 7696 q^{18} + 45352 q^{19} - 4096 q^{20} - 21296 q^{22} + 94736 q^{23} + 147846 q^{25} + 214912 q^{26} - 8528 q^{27} + 446692 q^{29} - 269248 q^{30} + 491552 q^{31} - 65536 q^{32} + 441892 q^{33} - 89760 q^{34} + 117992 q^{35} + 1123456 q^{36} - 83308 q^{37} - 251424 q^{38} - 2386136 q^{39} + 739328 q^{40} - 158652 q^{41} - 296352 q^{42} - 759368 q^{43} - 170368 q^{44} + 1083824 q^{45} + 1274496 q^{46} - 1539392 q^{47} + 212992 q^{48} + 4000066 q^{49} - 1210928 q^{50} + 8233888 q^{51} + 529664 q^{52} + 68580 q^{53} - 2201664 q^{54} - 2699268 q^{55} - 702464 q^{56} + 10864216 q^{57} + 1226144 q^{58} + 272372 q^{59} + 1343488 q^{60} - 3855420 q^{61} + 5872960 q^{62} + 3218712 q^{63} + 8912896 q^{64} + 11462480 q^{65} - 8878224 q^{67} + 988416 q^{68} - 3753160 q^{69} - 1372000 q^{70} + 3894464 q^{71} - 492544 q^{72} - 6269612 q^{73} - 2345312 q^{74} + 7329908 q^{75} + 2902528 q^{76} - 1826132 q^{77} - 1696832 q^{78} + 14769920 q^{79} - 262144 q^{80} - 20572462 q^{81} - 6603936 q^{82} - 16704880 q^{83} + 8502504 q^{85} - 13613184 q^{86} - 17013392 q^{87} - 1362944 q^{88} + 12658188 q^{89} + 31861984 q^{90} - 10733156 q^{91} + 6063104 q^{92} + 58199152 q^{93} + 4726080 q^{94} - 16029448 q^{95} + 10409332 q^{97} - 1882384 q^{98} + 7568066 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(154))\) 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
154.8.a.a 154.a 1.a $2$ $48.107$ \(\Q(\sqrt{449}) \) None \(16\) \(21\) \(-413\) \(686\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+(12-3\beta )q^{3}+2^{6}q^{4}+(-212+\cdots)q^{5}+\cdots\)
154.8.a.b 154.a 1.a $4$ $48.107$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(-35\) \(147\) \(-1372\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+(-9+\beta _{1})q^{3}+2^{6}q^{4}+(6^{2}+\cdots)q^{5}+\cdots\)
154.8.a.c 154.a 1.a $4$ $48.107$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(21\) \(-735\) \(-1372\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+(5+\beta _{1}+\beta _{2})q^{3}+2^{6}q^{4}+\cdots\)
154.8.a.d 154.a 1.a $4$ $48.107$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(-35\) \(133\) \(-1372\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(-9-\beta _{1})q^{3}+2^{6}q^{4}+(33+\cdots)q^{5}+\cdots\)
154.8.a.e 154.a 1.a $5$ $48.107$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-40\) \(-35\) \(-17\) \(1715\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+(-7+\beta _{1})q^{3}+2^{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)
154.8.a.f 154.a 1.a $5$ $48.107$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-40\) \(75\) \(-149\) \(1715\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+(15-\beta _{1})q^{3}+2^{6}q^{4}+(-30+\cdots)q^{5}+\cdots\)
154.8.a.g 154.a 1.a $5$ $48.107$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(-35\) \(719\) \(1715\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(-7+\beta _{1})q^{3}+2^{6}q^{4}+(12^{2}+\cdots)q^{5}+\cdots\)
154.8.a.h 154.a 1.a $5$ $48.107$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(75\) \(251\) \(-1715\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+(15-\beta _{1})q^{3}+2^{6}q^{4}+(50+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(154)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)