Properties

Label 1476.2.a
Level $1476$
Weight $2$
Character orbit 1476.a
Rep. character $\chi_{1476}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $7$
Sturm bound $504$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(504\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1476))\).

Total New Old
Modular forms 264 16 248
Cusp forms 241 16 225
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.

\(2\)\(3\)\(41\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 4q^{17} - 2q^{19} + 24q^{25} + 4q^{31} + 6q^{35} + 4q^{37} + 4q^{41} - 16q^{43} + 6q^{47} + 12q^{49} + 20q^{53} + 6q^{55} - 12q^{59} - 4q^{61} + 32q^{65} + 4q^{67} - 6q^{71} + 36q^{73} - 12q^{77} + 14q^{79} - 12q^{83} + 16q^{85} + 12q^{89} + 4q^{91} - 2q^{95} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1476))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 41
1476.2.a.a \(1\) \(11.786\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}+q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
1476.2.a.b \(1\) \(11.786\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(q+2q^{5}-4q^{7}+5q^{11}+4q^{13}+5q^{17}+\cdots\)
1476.2.a.c \(2\) \(11.786\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
1476.2.a.d \(2\) \(11.786\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+(2+\beta )q^{5}+(2-\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
1476.2.a.e \(3\) \(11.786\) 3.3.404.1 None \(0\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots\)
1476.2.a.f \(3\) \(11.786\) 3.3.404.1 None \(0\) \(0\) \(4\) \(4\) \(-\) \(+\) \(+\) \(q+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots\)
1476.2.a.g \(4\) \(11.786\) 4.4.25808.1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1476))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(492))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(738))\)\(^{\oplus 2}\)