Properties

Label 1904.2.a
Level $1904$
Weight $2$
Character orbit 1904.a
Rep. character $\chi_{1904}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $20$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1904.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1904))\).

Total New Old
Modular forms 300 48 252
Cusp forms 277 48 229
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.

\(2\)\(7\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(-\)\(-\)$+$\(6\)
\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(19\)
Minus space\(-\)\(29\)

Trace form

\( 48 q + 2 q^{7} + 48 q^{9} + O(q^{10}) \) \( 48 q + 2 q^{7} + 48 q^{9} - 8 q^{11} - 24 q^{15} + 16 q^{23} + 48 q^{25} - 8 q^{29} - 8 q^{37} + 40 q^{39} + 36 q^{43} - 24 q^{47} + 48 q^{49} - 12 q^{51} - 8 q^{53} + 8 q^{55} + 16 q^{57} + 24 q^{59} + 10 q^{63} + 16 q^{65} - 4 q^{67} + 32 q^{71} + 64 q^{75} - 8 q^{77} + 40 q^{79} + 64 q^{81} + 40 q^{83} + 56 q^{87} + 16 q^{89} - 12 q^{91} - 48 q^{93} + 48 q^{95} + 16 q^{97} + 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1904))\) 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 7 17
1904.2.a.a 1904.a 1.a $1$ $15.204$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
1904.2.a.b 1904.a 1.a $1$ $15.204$ \(\Q\) None \(0\) \(-2\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
1904.2.a.c 1904.a 1.a $1$ $15.204$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots\)
1904.2.a.d 1904.a 1.a $1$ $15.204$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots\)
1904.2.a.e 1904.a 1.a $1$ $15.204$ \(\Q\) None \(0\) \(2\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
1904.2.a.f 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1904.2.a.g 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-3\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
1904.2.a.h 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
1904.2.a.i 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.j 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.k 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}-4q^{11}+\cdots\)
1904.2.a.l 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
1904.2.a.m 1904.a 1.a $3$ $15.204$ 3.3.229.1 None \(0\) \(-1\) \(3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
1904.2.a.n 1904.a 1.a $3$ $15.204$ 3.3.1229.1 None \(0\) \(1\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1904.2.a.o 1904.a 1.a $3$ $15.204$ 3.3.229.1 None \(0\) \(3\) \(-5\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(-2-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.p 1904.a 1.a $3$ $15.204$ 3.3.229.1 None \(0\) \(3\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1904.2.a.q 1904.a 1.a $4$ $15.204$ 4.4.5225.1 None \(0\) \(-3\) \(-1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+q^{7}+\cdots\)
1904.2.a.r 1904.a 1.a $4$ $15.204$ 4.4.13448.1 None \(0\) \(-3\) \(5\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.s 1904.a 1.a $4$ $15.204$ 4.4.9301.1 None \(0\) \(-2\) \(2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1904.2.a.t 1904.a 1.a $5$ $15.204$ 5.5.453749.1 None \(0\) \(2\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 2}\)