Properties

Label 1334.2.a
Level $1334$
Weight $2$
Character orbit 1334.a
Rep. character $\chi_{1334}(1,\cdot)$
Character field $\Q$
Dimension $53$
Newform subspaces $11$
Sturm bound $360$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(360\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1334))\).

Total New Old
Modular forms 184 53 131
Cusp forms 177 53 124
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(23\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(19\)
Minus space\(-\)\(34\)

Trace form

\( 53q + q^{2} + 4q^{3} + 53q^{4} - 6q^{5} + 8q^{7} + q^{8} + 53q^{9} + O(q^{10}) \) \( 53q + q^{2} + 4q^{3} + 53q^{4} - 6q^{5} + 8q^{7} + q^{8} + 53q^{9} - 6q^{10} - 8q^{11} + 4q^{12} + 2q^{13} - 8q^{14} - 24q^{15} + 53q^{16} - 14q^{17} - 3q^{18} + 24q^{19} - 6q^{20} - 8q^{21} - q^{23} + 39q^{25} - 2q^{26} + 16q^{27} + 8q^{28} + 5q^{29} + 12q^{30} + q^{32} + 12q^{33} - 6q^{34} + 16q^{35} + 53q^{36} - 6q^{37} - 4q^{38} + 24q^{39} - 6q^{40} - 14q^{41} + 24q^{42} + 8q^{43} - 8q^{44} + 6q^{45} + 3q^{46} - 32q^{47} + 4q^{48} + 45q^{49} + 23q^{50} - 16q^{51} + 2q^{52} + 18q^{53} + 12q^{54} - 40q^{55} - 8q^{56} - 16q^{57} + q^{58} - 4q^{59} - 24q^{60} + 2q^{61} + 4q^{62} - 8q^{63} + 53q^{64} - 16q^{65} + 16q^{66} + 36q^{67} - 14q^{68} + 4q^{69} - 24q^{70} - 8q^{71} - 3q^{72} + 26q^{73} - 2q^{74} - 4q^{75} + 24q^{76} + 24q^{77} + 4q^{78} + 8q^{79} - 6q^{80} + 13q^{81} - 6q^{82} + 4q^{83} - 8q^{84} - 28q^{85} + 48q^{86} - 4q^{87} + 34q^{89} - 22q^{90} + 8q^{91} - q^{92} - 28q^{93} - 12q^{94} - 16q^{95} - 6q^{97} - 23q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23 29
1334.2.a.a \(1\) \(10.652\) \(\Q\) None \(-1\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots\)
1334.2.a.b \(1\) \(10.652\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-4q^{7}+\cdots\)
1334.2.a.c \(1\) \(10.652\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1334.2.a.d \(4\) \(10.652\) 4.4.37108.1 None \(-4\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1334.2.a.e \(4\) \(10.652\) 4.4.4352.1 None \(4\) \(-4\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1334.2.a.f \(5\) \(10.652\) 5.5.207184.1 None \(-5\) \(1\) \(-5\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1334.2.a.g \(5\) \(10.652\) 5.5.978400.1 None \(-5\) \(1\) \(3\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots\)
1334.2.a.h \(5\) \(10.652\) 5.5.179024.1 None \(5\) \(-3\) \(-5\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
1334.2.a.i \(8\) \(10.652\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(4\) \(0\) \(8\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots\)
1334.2.a.j \(9\) \(10.652\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-3\) \(5\) \(6\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots\)
1334.2.a.k \(10\) \(10.652\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(5\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 2}\)