Properties

Label 3800.2.a
Level $3800$
Weight $2$
Character orbit 3800.a
Rep. character $\chi_{3800}(1,\cdot)$
Character field $\Q$
Dimension $85$
Newform subspaces $31$
Sturm bound $1200$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(1200\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3800))\).

Total New Old
Modular forms 624 85 539
Cusp forms 577 85 492
Eisenstein series 47 0 47

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

\(2\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(14\)
Plus space\(+\)\(35\)
Minus space\(-\)\(50\)

Trace form

\( 85q - 4q^{7} + 79q^{9} + O(q^{10}) \) \( 85q - 4q^{7} + 79q^{9} + 6q^{11} - 2q^{13} + 6q^{17} + 3q^{19} + 16q^{21} + 6q^{23} + 30q^{29} - 12q^{31} + 20q^{33} + 14q^{37} + 22q^{39} + 14q^{41} + 2q^{43} + 6q^{47} + 81q^{49} + 20q^{51} + 14q^{53} + 2q^{57} - 8q^{59} + 16q^{61} + 6q^{63} - 4q^{67} - 4q^{69} + 40q^{71} + 18q^{73} - 14q^{77} - 36q^{79} + 101q^{81} - 20q^{83} - 18q^{87} + 30q^{89} + 12q^{93} - 6q^{97} - 14q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3800))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
3800.2.a.a \(1\) \(30.343\) \(\Q\) None \(0\) \(-3\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q-3q^{3}+q^{7}+6q^{9}+4q^{11}-q^{13}+\cdots\)
3800.2.a.b \(1\) \(30.343\) \(\Q\) None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-2q^{3}-4q^{7}+q^{9}-4q^{11}-6q^{17}+\cdots\)
3800.2.a.c \(1\) \(30.343\) \(\Q\) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}+8q^{17}+\cdots\)
3800.2.a.d \(1\) \(30.343\) \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots\)
3800.2.a.e \(1\) \(30.343\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{9}-4q^{11}+6q^{13}+6q^{17}-q^{19}+\cdots\)
3800.2.a.f \(1\) \(30.343\) \(\Q\) None \(0\) \(2\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+2q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
3800.2.a.g \(1\) \(30.343\) \(\Q\) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+2q^{3}-2q^{7}+q^{9}+4q^{11}-8q^{17}+\cdots\)
3800.2.a.h \(1\) \(30.343\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}-4q^{11}-4q^{13}+2q^{17}+\cdots\)
3800.2.a.i \(1\) \(30.343\) \(\Q\) None \(0\) \(2\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+2q^{3}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
3800.2.a.j \(2\) \(30.343\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{3}+(1-2\beta )q^{9}+2q^{11}+\cdots\)
3800.2.a.k \(2\) \(30.343\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+2\beta q^{7}+(3+2\beta )q^{9}+\cdots\)
3800.2.a.l \(2\) \(30.343\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+(1-\beta )q^{7}-2\beta q^{9}+\cdots\)
3800.2.a.m \(2\) \(30.343\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+\beta q^{3}+(-2+2\beta )q^{7}-q^{9}+(2-2\beta )q^{11}+\cdots\)
3800.2.a.n \(2\) \(30.343\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{3}+2\beta q^{7}-q^{9}+(2-2\beta )q^{11}+\cdots\)
3800.2.a.o \(2\) \(30.343\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+\beta q^{3}+(2+2\beta )q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots\)
3800.2.a.p \(2\) \(30.343\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots\)
3800.2.a.q \(2\) \(30.343\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}-2\beta q^{7}+(3+2\beta )q^{9}+(-1+\cdots)q^{13}+\cdots\)
3800.2.a.r \(3\) \(30.343\) 3.3.961.1 None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{7}+(5-\beta _{1}+\cdots)q^{9}+\cdots\)
3800.2.a.s \(3\) \(30.343\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
3800.2.a.t \(3\) \(30.343\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
3800.2.a.u \(3\) \(30.343\) 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{2}q^{3}-\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3800.2.a.v \(3\) \(30.343\) 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{2}q^{3}+\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3800.2.a.w \(3\) \(30.343\) 3.3.316.1 None \(0\) \(1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(1-2\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
3800.2.a.x \(3\) \(30.343\) 3.3.229.1 None \(0\) \(1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q-\beta _{2}q^{3}-\beta _{1}q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{13}+\cdots\)
3800.2.a.y \(3\) \(30.343\) 3.3.568.1 None \(0\) \(1\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
3800.2.a.z \(6\) \(30.343\) 6.6.253565184.1 None \(0\) \(-2\) \(0\) \(-6\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
3800.2.a.ba \(6\) \(30.343\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
3800.2.a.bb \(6\) \(30.343\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
3800.2.a.bc \(6\) \(30.343\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4})q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
3800.2.a.bd \(6\) \(30.343\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
3800.2.a.be \(6\) \(30.343\) 6.6.253565184.1 None \(0\) \(2\) \(0\) \(6\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1900))\)\(^{\oplus 2}\)