Properties

Label 2898.2.a
Level $2898$
Weight $2$
Character orbit 2898.a
Rep. character $\chi_{2898}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $35$
Sturm bound $1152$
Trace bound $11$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2898.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2898))\).

Total New Old
Modular forms 592 56 536
Cusp forms 561 56 505
Eisenstein series 31 0 31

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

\(2\)\(3\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(22\)
Minus space\(-\)\(34\)

Trace form

\( 56q + 56q^{4} + 4q^{5} + O(q^{10}) \) \( 56q + 56q^{4} + 4q^{5} + 4q^{10} - 12q^{11} + 4q^{13} + 56q^{16} + 12q^{19} + 4q^{20} + 12q^{22} + 64q^{25} + 12q^{26} - 8q^{29} - 16q^{31} + 24q^{34} - 4q^{35} - 12q^{37} - 28q^{38} + 4q^{40} + 16q^{41} + 4q^{43} - 12q^{44} + 4q^{46} - 24q^{47} + 56q^{49} + 8q^{50} + 4q^{52} + 36q^{53} + 8q^{58} + 4q^{59} - 28q^{61} + 16q^{62} + 56q^{64} - 24q^{65} + 4q^{67} + 4q^{70} + 32q^{71} + 24q^{73} + 28q^{74} + 12q^{76} + 8q^{77} + 16q^{79} + 4q^{80} + 32q^{82} + 28q^{83} + 72q^{85} - 20q^{86} + 12q^{88} + 8q^{89} + 24q^{91} - 8q^{94} + 48q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 23
2898.2.a.a \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
2898.2.a.b \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
2898.2.a.c \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
2898.2.a.d \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
2898.2.a.e \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2898.2.a.f \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.g \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.h \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.i \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.j \(1\) \(23.141\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
2898.2.a.k \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
2898.2.a.l \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
2898.2.a.m \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2898.2.a.n \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\)
2898.2.a.o \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
2898.2.a.p \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+q^{14}+\cdots\)
2898.2.a.q \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
2898.2.a.r \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
2898.2.a.s \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2898.2.a.t \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
2898.2.a.u \(1\) \(23.141\) \(\Q\) None \(1\) \(0\) \(4\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots\)
2898.2.a.v \(2\) \(23.141\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
2898.2.a.w \(2\) \(23.141\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
2898.2.a.x \(2\) \(23.141\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(3\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.y \(2\) \(23.141\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.z \(2\) \(23.141\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2898.2.a.ba \(2\) \(23.141\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-\beta q^{5}-q^{7}+q^{8}-\beta q^{10}+\cdots\)
2898.2.a.bb \(2\) \(23.141\) \(\Q(\sqrt{41}) \) None \(2\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-\beta q^{5}+q^{7}+q^{8}-\beta q^{10}+\cdots\)
2898.2.a.bc \(2\) \(23.141\) \(\Q(\sqrt{41}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2898.2.a.bd \(2\) \(23.141\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2898.2.a.be \(3\) \(23.141\) 3.3.316.1 None \(-3\) \(0\) \(-4\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.bf \(3\) \(23.141\) 3.3.568.1 None \(-3\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{7}-q^{8}-\beta _{2}q^{10}+\cdots\)
2898.2.a.bg \(3\) \(23.141\) 3.3.568.1 None \(3\) \(0\) \(1\) \(-3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-\beta _{2}q^{5}-q^{7}+q^{8}-\beta _{2}q^{10}+\cdots\)
2898.2.a.bh \(4\) \(23.141\) 4.4.271296.1 None \(-4\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}+q^{7}-q^{8}-\beta _{1}q^{10}+\cdots\)
2898.2.a.bi \(4\) \(23.141\) 4.4.271296.1 None \(4\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2898))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2898)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 2}\)