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Properties

Label 2151.4.a
Level $2151$
Weight $4$
Character orbit 2151.a
Rep. character $\chi_{2151}(1,\cdot)$
Character field $\Q$
Dimension $297$
Newform subspaces $8$
Sturm bound $960$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(960\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2151))\).

Total New Old
Modular forms 724 297 427
Cusp forms 716 297 419
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.

\(3\)\(239\)FrickeDim.
\(+\)\(+\)\(+\)\(59\)
\(+\)\(-\)\(-\)\(59\)
\(-\)\(+\)\(-\)\(82\)
\(-\)\(-\)\(+\)\(97\)
Plus space\(+\)\(156\)
Minus space\(-\)\(141\)

Trace form

\( 297q + 4q^{2} + 1196q^{4} + 10q^{5} - 32q^{7} + 6q^{8} + O(q^{10}) \) \( 297q + 4q^{2} + 1196q^{4} + 10q^{5} - 32q^{7} + 6q^{8} - 90q^{10} - 34q^{11} + 172q^{13} - 118q^{14} + 4612q^{16} - 122q^{17} - 38q^{19} + 464q^{20} + 4q^{22} - 192q^{23} + 7439q^{25} + 180q^{26} - 62q^{28} + 262q^{29} - 750q^{31} - 198q^{32} - 162q^{34} - 160q^{35} + 196q^{37} - 494q^{38} - 936q^{40} - 322q^{41} + 170q^{43} + 170q^{44} - 4q^{46} - 440q^{47} + 13397q^{49} + 1158q^{50} + 1742q^{52} - 452q^{53} - 1484q^{55} - 360q^{56} - 360q^{58} - 242q^{59} - 690q^{61} + 269q^{62} + 18838q^{64} - 340q^{65} + 1502q^{67} - 1432q^{68} + 1180q^{70} + 1434q^{71} - 3838q^{73} + 810q^{74} + 1022q^{76} + 212q^{77} - 984q^{79} + 5451q^{80} + 1062q^{82} + 1210q^{83} + 264q^{85} + 1734q^{86} + 1252q^{88} + 1410q^{89} + 3716q^{91} - 1456q^{92} - 2202q^{94} + 2096q^{95} + 4438q^{97} + 4926q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2151))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 239
2151.4.a.a \(22\) \(126.913\) None \(4\) \(0\) \(37\) \(-52\) \(-\) \(+\)
2151.4.a.b \(28\) \(126.913\) None \(5\) \(0\) \(-6\) \(-68\) \(-\) \(+\)
2151.4.a.c \(28\) \(126.913\) None \(13\) \(0\) \(74\) \(-82\) \(-\) \(-\)
2151.4.a.d \(32\) \(126.913\) None \(-11\) \(0\) \(-66\) \(58\) \(-\) \(+\)
2151.4.a.e \(32\) \(126.913\) None \(-3\) \(0\) \(14\) \(72\) \(-\) \(-\)
2151.4.a.f \(37\) \(126.913\) None \(-4\) \(0\) \(-43\) \(60\) \(-\) \(-\)
2151.4.a.g \(59\) \(126.913\) None \(-8\) \(0\) \(-80\) \(-10\) \(+\) \(-\)
2151.4.a.h \(59\) \(126.913\) None \(8\) \(0\) \(80\) \(-10\) \(+\) \(+\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2151))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2151)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(717))\)\(^{\oplus 2}\)