Properties

Label 2150.2.a
Level $2150$
Weight $2$
Character orbit 2150.a
Rep. character $\chi_{2150}(1,\cdot)$
Character field $\Q$
Dimension $67$
Newform subspaces $34$
Sturm bound $660$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2150 = 2 \cdot 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 34 \)
Sturm bound: \(660\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2150))\).

Total New Old
Modular forms 342 67 275
Cusp forms 319 67 252
Eisenstein series 23 0 23

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

\(2\)\(5\)\(43\)FrickeDim
\(+\)\(+\)\(+\)$+$\(7\)
\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(-\)\(+\)$-$\(11\)
\(+\)\(-\)\(-\)$+$\(7\)
\(-\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(6\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(26\)
Minus space\(-\)\(41\)

Trace form

\( 67 q + q^{2} + 4 q^{3} + 67 q^{4} + 2 q^{6} + 4 q^{7} + q^{8} + 81 q^{9} + O(q^{10}) \) \( 67 q + q^{2} + 4 q^{3} + 67 q^{4} + 2 q^{6} + 4 q^{7} + q^{8} + 81 q^{9} + 12 q^{11} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 67 q^{16} + 5 q^{18} + 4 q^{21} + 8 q^{22} - 6 q^{23} + 2 q^{24} - 18 q^{26} + 4 q^{27} + 4 q^{28} - 26 q^{29} + 14 q^{31} + q^{32} - 24 q^{33} - 10 q^{34} + 81 q^{36} + 34 q^{37} - 10 q^{38} - 4 q^{41} - q^{43} + 12 q^{44} + 12 q^{46} - 22 q^{47} + 4 q^{48} + 83 q^{49} + 4 q^{51} + 2 q^{52} - 30 q^{53} - 16 q^{54} + 4 q^{56} + 16 q^{57} + 20 q^{58} - 4 q^{59} + 10 q^{61} - 20 q^{62} + 24 q^{63} + 67 q^{64} + 8 q^{66} + 36 q^{67} - 52 q^{69} - 56 q^{71} + 5 q^{72} - 22 q^{73} - 8 q^{74} + 16 q^{77} + 12 q^{78} + 26 q^{79} + 75 q^{81} + 18 q^{82} - 4 q^{83} + 4 q^{84} + 5 q^{86} + 42 q^{87} + 8 q^{88} - 90 q^{89} + 120 q^{91} - 6 q^{92} + 4 q^{94} + 2 q^{96} + 52 q^{97} - 7 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2150))\) 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 5 43
2150.2.a.a 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(-3\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
2150.2.a.b 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(-2\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots\)
2150.2.a.c 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
2150.2.a.d 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}-3q^{9}+5q^{11}+\cdots\)
2150.2.a.e 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
2150.2.a.f 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(2\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
2150.2.a.g 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(2\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+5q^{7}-q^{8}+\cdots\)
2150.2.a.h 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(3\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+2q^{7}-q^{8}+\cdots\)
2150.2.a.i 2150.a 1.a $1$ $17.168$ \(\Q\) None \(-1\) \(3\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots\)
2150.2.a.j 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(-3\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-4q^{7}+q^{8}+\cdots\)
2150.2.a.k 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(-3\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-2q^{7}+q^{8}+\cdots\)
2150.2.a.l 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
2150.2.a.m 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}-3q^{9}+5q^{11}+\cdots\)
2150.2.a.n 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-4q^{11}+\cdots\)
2150.2.a.o 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{7}+q^{8}-3q^{9}+3q^{13}+\cdots\)
2150.2.a.p 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
2150.2.a.q 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-4q^{7}+q^{8}+\cdots\)
2150.2.a.r 2150.a 1.a $1$ $17.168$ \(\Q\) None \(1\) \(3\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
2150.2.a.s 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
2150.2.a.t 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-2+4\beta )q^{7}+\cdots\)
2150.2.a.u 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(0\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-4q^{7}-q^{8}+\cdots\)
2150.2.a.v 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
2150.2.a.w 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
2150.2.a.x 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
2150.2.a.y 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+4q^{7}+q^{8}+\cdots\)
2150.2.a.z 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{21}) \) None \(2\) \(1\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-2q^{7}+q^{8}+\cdots\)
2150.2.a.ba 2150.a 1.a $2$ $17.168$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
2150.2.a.bb 2150.a 1.a $3$ $17.168$ 3.3.568.1 None \(-3\) \(1\) \(0\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots\)
2150.2.a.bc 2150.a 1.a $3$ $17.168$ 3.3.148.1 None \(-3\) \(2\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
2150.2.a.bd 2150.a 1.a $3$ $17.168$ 3.3.148.1 None \(3\) \(-2\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
2150.2.a.be 2150.a 1.a $3$ $17.168$ 3.3.568.1 None \(3\) \(-1\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
2150.2.a.bf 2150.a 1.a $3$ $17.168$ 3.3.316.1 None \(3\) \(2\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
2150.2.a.bg 2150.a 1.a $8$ $17.168$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-4\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
2150.2.a.bh 2150.a 1.a $8$ $17.168$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(4\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1075))\)\(^{\oplus 2}\)