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Properties

Label 154.4.k
Level $154$
Weight $4$
Character orbit 154.k
Rep. character $\chi_{154}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $96$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96 q + 96 q^{4} + 20 q^{7} + 312 q^{9} + O(q^{10}) \) \( 96 q + 96 q^{4} + 20 q^{7} + 312 q^{9} - 36 q^{11} + 52 q^{14} - 372 q^{15} - 384 q^{16} - 184 q^{22} + 392 q^{23} - 124 q^{25} + 120 q^{28} - 700 q^{29} + 1010 q^{35} - 608 q^{36} - 720 q^{37} + 460 q^{39} - 716 q^{42} - 976 q^{44} + 402 q^{49} + 3620 q^{51} - 896 q^{53} - 128 q^{56} + 560 q^{57} + 1680 q^{58} - 992 q^{60} + 6440 q^{63} + 1536 q^{64} + 3552 q^{67} + 168 q^{70} - 3880 q^{71} - 2240 q^{72} - 2800 q^{74} - 7262 q^{77} - 1920 q^{78} - 4200 q^{79} - 7816 q^{81} - 400 q^{84} - 6940 q^{85} + 104 q^{86} + 1856 q^{88} + 2514 q^{91} + 1792 q^{92} + 8340 q^{93} - 1560 q^{95} + 11460 q^{99} + O(q^{100}) \)

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.k.a 154.k 77.l $96$ $9.086$ None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{10}]$

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

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