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Properties

Label 1506.2.a
Level $1506$
Weight $2$
Character orbit 1506.a
Rep. character $\chi_{1506}(1,\cdot)$
Character field $\Q$
Dimension $43$
Newform subspaces $16$
Sturm bound $504$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1506 = 2 \cdot 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1506.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(504\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1506))\).

Total New Old
Modular forms 256 43 213
Cusp forms 249 43 206
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.

\(2\)\(3\)\(251\)FrickeDim
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(16\)
Minus space\(-\)\(27\)

Trace form

\( 43 q + q^{2} + q^{3} + 43 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 43 q^{9} + O(q^{10}) \) \( 43 q + q^{2} + q^{3} + 43 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 43 q^{9} - 2 q^{10} - 12 q^{11} + q^{12} + 6 q^{13} + 2 q^{15} + 43 q^{16} + 2 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{22} + 8 q^{23} - q^{24} + 61 q^{25} + 6 q^{26} + q^{27} - 4 q^{28} + 30 q^{29} + 2 q^{30} + 12 q^{31} + q^{32} + 4 q^{33} - 6 q^{34} - 16 q^{35} + 43 q^{36} + 2 q^{37} - 4 q^{38} + 6 q^{39} - 2 q^{40} - 14 q^{41} - 8 q^{42} - 12 q^{44} - 2 q^{45} - 16 q^{46} - 32 q^{47} + q^{48} + 55 q^{49} - q^{50} + 10 q^{51} + 6 q^{52} + 14 q^{53} - q^{54} + 16 q^{57} + 2 q^{58} - 4 q^{59} + 2 q^{60} + 10 q^{61} - 16 q^{62} - 4 q^{63} + 43 q^{64} - 20 q^{65} - 4 q^{66} + 4 q^{67} + 2 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} + 15 q^{75} + 8 q^{76} - 64 q^{77} + 2 q^{78} - 20 q^{79} - 2 q^{80} + 43 q^{81} - 6 q^{82} - 20 q^{83} + 8 q^{84} + 44 q^{85} - 20 q^{86} + 18 q^{87} + 8 q^{88} - 6 q^{89} - 2 q^{90} - 8 q^{91} + 8 q^{92} + 8 q^{93} + 24 q^{94} - 8 q^{95} - q^{96} - 10 q^{97} + 9 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\) 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 3 251
1506.2.a.a 1506.a 1.a $1$ $12.025$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-2q^{7}+\cdots\)
1506.2.a.b 1506.a 1.a $1$ $12.025$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
1506.2.a.c 1506.a 1.a $1$ $12.025$ \(\Q\) None \(-1\) \(1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
1506.2.a.d 1506.a 1.a $1$ $12.025$ \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
1506.2.a.e 1506.a 1.a $1$ $12.025$ \(\Q\) None \(1\) \(1\) \(-4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-4q^{7}+\cdots\)
1506.2.a.f 1506.a 1.a $1$ $12.025$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
1506.2.a.g 1506.a 1.a $1$ $12.025$ \(\Q\) None \(1\) \(1\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
1506.2.a.h 1506.a 1.a $1$ $12.025$ \(\Q\) None \(1\) \(1\) \(4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1506.2.a.i 1506.a 1.a $2$ $12.025$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
1506.2.a.j 1506.a 1.a $2$ $12.025$ \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(2+\beta )q^{7}+\cdots\)
1506.2.a.k 1506.a 1.a $4$ $12.025$ \(\Q(\zeta_{20})^+\) None \(-4\) \(-4\) \(2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1506.2.a.l 1506.a 1.a $5$ $12.025$ 5.5.11159660.1 None \(-5\) \(5\) \(2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{4})q^{5}-q^{6}+\cdots\)
1506.2.a.m 1506.a 1.a $5$ $12.025$ 5.5.176684.1 None \(5\) \(-5\) \(-8\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1506.2.a.n 1506.a 1.a $5$ $12.025$ 5.5.2950792.1 None \(5\) \(5\) \(2\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots\)
1506.2.a.o 1506.a 1.a $6$ $12.025$ 6.6.55941992.1 None \(-6\) \(-6\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(\beta _{2}-\beta _{3})q^{5}+q^{6}+\cdots\)
1506.2.a.p 1506.a 1.a $6$ $12.025$ 6.6.146527424.1 None \(6\) \(-6\) \(6\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1506))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1506)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 2}\)