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Properties

Label 1155.2.a
Level $1155$
Weight $2$
Character orbit 1155.a
Rep. character $\chi_{1155}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $23$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1155))\).

Total New Old
Modular forms 200 41 159
Cusp forms 185 41 144
Eisenstein series 15 0 15

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

\(3\)\(5\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(-\)\(+\)\(+\)$-$\(3\)
\(+\)\(-\)\(+\)\(-\)$+$\(3\)
\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(-\)$+$\(2\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(5\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(3\)
\(-\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(13\)
Minus space\(-\)\(28\)

Trace form

\( 41 q + 3 q^{2} + q^{3} + 39 q^{4} + q^{5} - 5 q^{6} + q^{7} + 15 q^{8} + 41 q^{9} + O(q^{10}) \) \( 41 q + 3 q^{2} + q^{3} + 39 q^{4} + q^{5} - 5 q^{6} + q^{7} + 15 q^{8} + 41 q^{9} - 5 q^{10} + q^{11} + 7 q^{12} + 14 q^{13} + 3 q^{14} - 7 q^{15} + 47 q^{16} + 2 q^{17} + 3 q^{18} - 12 q^{19} + 7 q^{20} + q^{21} - 5 q^{22} - 8 q^{23} - 9 q^{24} + 41 q^{25} + 26 q^{26} + q^{27} + 7 q^{28} + 14 q^{29} + 3 q^{30} + 63 q^{32} + q^{33} + 38 q^{34} + q^{35} + 39 q^{36} + 6 q^{37} + 12 q^{38} + 14 q^{39} - 9 q^{40} - 6 q^{41} - 5 q^{42} + 12 q^{43} + 7 q^{44} + q^{45} + 8 q^{46} + 31 q^{48} + 41 q^{49} + 3 q^{50} - 14 q^{51} + 98 q^{52} + 6 q^{53} - 5 q^{54} + q^{55} + 15 q^{56} + 20 q^{57} + 42 q^{58} - 4 q^{59} - 17 q^{60} - 2 q^{61} - 64 q^{62} + q^{63} + 15 q^{64} - 2 q^{65} + 3 q^{66} - 28 q^{67} - 34 q^{68} - 24 q^{69} - 5 q^{70} - 56 q^{71} + 15 q^{72} + 10 q^{73} - 94 q^{74} + q^{75} - 36 q^{76} + q^{77} + 10 q^{78} - 16 q^{79} - 33 q^{80} + 41 q^{81} - 2 q^{82} - 28 q^{83} + 7 q^{84} - 14 q^{85} + 4 q^{86} - 18 q^{87} - 9 q^{88} + 10 q^{89} - 5 q^{90} - 2 q^{91} - 40 q^{92} + 16 q^{93} - 32 q^{94} + 4 q^{95} + 7 q^{96} - 14 q^{97} + 3 q^{98} + q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7 11
1155.2.a.a 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-2\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
1155.2.a.b 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-2\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.c 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-2\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1155.2.a.d 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.e 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.f 1155.a 1.a $1$ $9.223$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.g 1155.a 1.a $1$ $9.223$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1155.2.a.h 1155.a 1.a $1$ $9.223$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.i 1155.a 1.a $1$ $9.223$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.j 1155.a 1.a $1$ $9.223$ \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.k 1155.a 1.a $1$ $9.223$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.l 1155.a 1.a $1$ $9.223$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.m 1155.a 1.a $1$ $9.223$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
1155.2.a.n 1155.a 1.a $1$ $9.223$ \(\Q\) None \(2\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.o 1155.a 1.a $2$ $9.223$ \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
1155.2.a.p 1155.a 1.a $2$ $9.223$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
1155.2.a.q 1155.a 1.a $2$ $9.223$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
1155.2.a.r 1155.a 1.a $2$ $9.223$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
1155.2.a.s 1155.a 1.a $3$ $9.223$ 3.3.316.1 None \(1\) \(-3\) \(3\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.a.t 1155.a 1.a $3$ $9.223$ 3.3.316.1 None \(1\) \(3\) \(3\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.u 1155.a 1.a $4$ $9.223$ 4.4.13448.1 None \(0\) \(4\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.v 1155.a 1.a $4$ $9.223$ 4.4.7232.1 None \(2\) \(-4\) \(4\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
1155.2.a.w 1155.a 1.a $5$ $9.223$ 5.5.352076.1 None \(1\) \(5\) \(-5\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1155))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1155)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 2}\)