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Properties

Label 1914.2.a
Level $1914$
Weight $2$
Character orbit 1914.a
Rep. character $\chi_{1914}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $27$
Sturm bound $720$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1914 = 2 \cdot 3 \cdot 11 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1914.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(720\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1914))\).

Total New Old
Modular forms 368 45 323
Cusp forms 353 45 308
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.

\(2\)\(3\)\(11\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(-\)\(+\)\(+\)$-$\(2\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(1\)
\(+\)\(-\)\(-\)\(-\)$-$\(5\)
\(-\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(6\)
\(-\)\(-\)\(+\)\(+\)$+$\(2\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(34\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1914))\) 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 11 29
1914.2.a.a 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+3q^{7}+\cdots\)
1914.2.a.b 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1914.2.a.c 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1914.2.a.d 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1914.2.a.e 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
1914.2.a.f 1914.a 1.a $1$ $15.283$ \(\Q\) None \(-1\) \(1\) \(3\) \(-3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-3q^{7}+\cdots\)
1914.2.a.g 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-4q^{7}+\cdots\)
1914.2.a.h 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1914.2.a.i 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
1914.2.a.j 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(-1\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+5q^{7}+\cdots\)
1914.2.a.k 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1914.2.a.l 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(-1\) \(4\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
1914.2.a.m 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
1914.2.a.n 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
1914.2.a.o 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(1\) \(1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1914.2.a.p 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(1\) \(1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1914.2.a.q 1914.a 1.a $1$ $15.283$ \(\Q\) None \(1\) \(1\) \(4\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
1914.2.a.r 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+\beta q^{7}+\cdots\)
1914.2.a.s 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(2\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
1914.2.a.t 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-1\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1914.2.a.u 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
1914.2.a.v 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots\)
1914.2.a.w 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1914.2.a.x 1914.a 1.a $2$ $15.283$ \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(-1\) \(-3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
1914.2.a.y 1914.a 1.a $4$ $15.283$ 4.4.54764.1 None \(-4\) \(-4\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1914.2.a.z 1914.a 1.a $4$ $15.283$ 4.4.19664.1 None \(4\) \(4\) \(4\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)
1914.2.a.ba 1914.a 1.a $6$ $15.283$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(-6\) \(3\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1914))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1914)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(319))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(638))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(957))\)\(^{\oplus 2}\)